<figure><img src="image_10.png" /><figcaption>**Figure 6.** The density (illustrated by varying transparency) of $g_{\text{fiber}} < 24.1$ objects using Legacy imaging photometry. Each point is color-coded by the mean photometric redshift ($z_{\text{phot}}$) from the Hyper Suprime-Cam (HSC)/Gaia Data Data Release 2 (DR2; Aihara et al. 2019). The selection boundaries of the ELG\_LOP sample are illustrated by the black lines while the extended selection associated with the ELG\_VLO sample is represented by the red dashed lines. The green and red tracks demonstrate the redshift evolution (Bruzual & Charlot 2003) of a star-forming and passive galaxy, respectively. The symbols represent different epochs in that evolution: $z = 2$ (square), $z = 1.6$ (downward facing triangle), $z = 1.1$ (circle), $z = 0.6$ (upward facing triangle), and $z = 0.1$ (star).</figcaption></figure>

size and to limit the number of low-redshift galaxies. The boundary for the ELG\_LOP is set where the median redshift is approximately equal to $z = 1.1$ so that higher-redshift galaxies are favored. This boundary is shifted to redder colors for the ELG\_VLO sample to pick up objects around $z = 1$ that were shown in target selection validation to be spectroscopically classified at high efficiency.

A large part of the ELG sample overlaps in redshift with the LRG sample. This overlap will facilitate cross-correlation studies between the two tracers. However, this overlap also means that ELGs clustered with LRGs will compete for the same fibers. In the main program, we assign a higher priority to LRG targets than either the ELG\_LOP or ELG\_VLO samples, leading to a fairly high completeness in LRG targets at the cost of lower completeness in ELG targets. In order to obtain statistics on the ELG targets that typically get bumped by higher priority LRG targets, we increase the priority of 10% of all ELG targets to be identical to the priority of LRG. Fiber assignment between two objects of equal priority gets resolved by a random number generator, thus allowing a full characterization of completeness using mock catalogs as in Mohammad et al. (2020).

In the main survey, the ELG\_LOP sample will achieve a fiber assignment efficiency of 69% while the ELG\_VLO sample will achieve a fiber assignment efficiency of 42% after taking failed spectra into account.

## 4.6. Quasars (QSO)

The selection of quasar samples has historically relied on identification through excess UV emission (Richards et al. 2002; Ross et al. 2012). In DESI, we use an alternative approach that relies on flux excess in NIR bandpasses instead, as demonstrated in eBOSS (Myers et al. 2015). We use three optical bands ($g$, $r$, $z$) combined with W1 and W2 photometry to select our primary sample of quasars. The separation between stars and quasars allowed by optical and infrared

<figure><img src="image_11.png" /><figcaption>**Figure 7.** Colors in the optical and near-infrared for objects photometrically classified as stars (red) and spectroscopically classified as quasars. Quasar redshifts are color-coded as described in the sidebar. Here, $grz$ is the magnitude corresponding to the weighted flux defined as $\text{flux}(grz) = [\text{flux}(g) + 0.8 \times \text{flux}(r) + 0.5 \times \text{flux}(z)] / 2.3$. W is the magnitude corresponding to a weighted flux average defined as $\text{flux}(W) = 0.75 \times \text{flux}(W1) + 0.25 \times \text{flux}(W2)$.</figcaption></figure>

colors is illustrated in Figure 7. The relatively blue color of stars is due to the rapidly declining tail of the blackbody spectrum at infrared wavelengths. The relatively red color of quasars is due to the onset of infrared emission from the dusty torus (Hickox & Alexander 2018), leading to a flatter SED.

For BOSS observations, an algorithm based on a neural network for selecting quasars was found to increase the selection efficiency by approximately 20% compared to a selection based on strict boundaries in color and magnitude (Yèche et al. 2010). To further improve the efficiency of target selection for DESI, we use a new machine-learning algorithm based on RF. At a fixed density, the observations from the target selection validation program demonstrated that the RF produced 15% more quasars than the alternate color selection, including 21% more quasars at $z > 2.1$ for Ly-$\alpha$ forest measurements. The RF selection was therefore chosen for the main selection of quasars.

Before utilizing the RF, we only include objects that have stellar morphology (PSF) as identified in the legacy imaging. This rejection reduces contamination from extended source galaxies by an order of magnitude. We also require targets to have $16.5 < r_{AB} < 23.0$, with the bright limit set to remove residual stars and the faint limit set to ensure high-quality spectral data. Finally, to further reject stars with low infrared flux, we require $W1 < 22.3$ and $W2 < 22.3$. To obtain training samples not biased by anterior color selections, we initially used quasars selected by their intrinsic time-variability (Palanque-Delabrouille et al. 2011) in SDSS and “stars” that exhibited no significant variation in their SDSS light curves. This selection was used for the target selection validation target sample. We then retrained the RF selection on DESI spectra using 11 input parameters: the 10 possible colors using the five optical and NIR bands $grzW1W2$, and the $r$-band magnitude. By using correlated parameters in the 10 color measurements, the RF is trained to assign more or less importance to each input parameter.

Finally, the RF probabilities were tuned to obtain quasar targets, leading to a sample of targets at $\sim 310 \text{ deg}^{-2}$. To ensure a uniform target density over the full DESI footprint, we apply slightly different $r$-dependent thresholds on the RF probability in the three regions (north; south, DES; and south, non-DES; for more details, see Chaussidon et al. 2023). Because quasar targets will be given the highest priority during the 5 yr
<figure><img src="image_11.png" /><figcaption>**Figure 8.** The field centers for the 20 rosette pointings in the One-Percent Survey, with same shading scheme as in Figure 1.</figcaption></figure>

program, the fiber assignment efficiency will be 99%. In addition, the quasars classified at $z > 2.1$ after a single epoch of observation will be prioritized for up to four observations. Simulations of fiber assignment indicate that, on average, a $z > 2.1$ quasar will receive 3.4 epochs of observation, leading to increased signal-to-noise in the measurements of the Ly-$\alpha$ flux density field.

## 4.7. One-Percent Survey

Immediately after the target selection validation program, the One-Percent Survey was completed to obtain a DESI-like sample across all target classes. These data were used to determine the efficiency of automated routines for data acquisition and to create a sample that was highly complete in both fiber assignment and redshift classification in all target classes over roughly 1% of the final DESI footprint. The clustering measured in these data will be used to calibrate the halo occupation statistics in the DESI mock catalogs, allow early clustering measurements, and provide a sample that is comparable in size to previous spectroscopic programs for studies of stellar, galaxy, and quasar physics, but to fainter magnitudes. The footprint of these observations can be found in Figure 8, and details of the targeted fields are given in Table 3.

The target selection algorithms for the One-Percent Survey were nearly the same as those for the 5 yr program, with only two minor modifications. First, the magnitude limit in the selection algorithm for the BGS Faint sample was increased to $r < 20.3$, rather than $r < 20.175$ as in the main survey. This led to an increase in the total surface density of the BGS Bright and the BGS Faint samples to $1,480 \text{ deg}^{-2}$ in the One-Percent Survey. Second, the selection algorithm for LRG targets was modified to be somewhat more inclusive in the One-Percent Survey. The faint limit was moved 0.1 mag fainter in $z_{\text{fiber}}$, and the sliding cut in $r$-W1 versus W1 was moved to include slightly fainter galaxies. The color-color cut in $g - r$ versus $r$-W1 was also shifted toward slightly bluer colors to increase the number density of lower-redshift galaxies.

The observations for the One-Percent Survey were conducted in nearly the same mode as expected for the 5 yr program. The summary of observations can be found in Table 1.

LRG, ELG, and quasar targets were observed during the times when sky background, seeing, and transparency were most conducive to spectroscopy of faint sources. In most cases, these targets were observed using the automated field selection when conditions indicated at least a 40% survey speed. To achieve the goal of very high completeness in all target classes, the tiling pattern followed a rosette pattern over 20 unique field centers. Each rosette consisted of at least 12 individual tiles offset by 0.12° from the field center. A minimum of 11 these tiles were observed for each rosette. Targets within a $7.0 \text{ deg}^2$ annulus had significant coverage, while those targets over an additional $2 \text{ deg}^2$ were observed with fewer visits and lower completeness in fiber assignment. Up to three additional visits were given to targets that produced spectra without secure redshift estimates. These additional visits were assigned only if there were no unobserved LRG, ELG, or quasar targets competing for the fiber. Over the regions between 0.2° and 1.45° from the field center, spectra were successfully obtained for 99% of LRG targets, 95% of ELG targets, and nearly 100% of quasar targets. The completeness statistics for each field are found in Table 3, and the completeness as a function of pairwise separation is presented in Figure 9. At such a high completeness in fiber assignment, the primary LRG sample for the main survey is nearly fully covered, even with the extensions described above.

BGS and MWS targets were observed during the times with slightly degraded conditions, where good signal-to-noise would still be achieved due to the higher source fluxes. In some cases, BGS and MWS tiles were observed during conditions that would have otherwise been considered for LRG, ELG, quasar observations because we needed the tiles to fill the observing queue for the entire night. The same rosette pattern was used for these targets, but with a minimum of 10 to be observed for each field. Spectroscopy was obtained for 99% for BGS Bright and for BGS Faint, and 96% for MWS targets. As with the
<figure><img src="image_12.png" /><figcaption>**Figure 8.** The field centers for the 20 rosette pointings in the One-Percent Survey, with same shading scheme as in Figure 1.</figcaption></figure>

program, the fiber assignment efficiency will be 99%. In addition, the quasars classified at $z > 2.1$ after a single epoch of observation will be prioritized for up to four observations. Simulations of fiber assignment indicate that, on average, a $z > 2.1$ quasar will receive 3.4 epochs of observation, leading to increased signal-to-noise in the measurements of the Ly-$\alpha$ flux density field.

## 4.7. One-Percent Survey

Immediately after the target selection validation program, the One-Percent Survey was completed to obtain a DESI-like sample across all target classes. These data were used to determine the efficiency of automated routines for data acquisition and to create a sample that was highly complete in both fiber assignment and redshift classification in all target classes over roughly 1% of the final DESI footprint. The clustering measured in these data will be used to calibrate the halo occupation statistics in the DESI mock catalogs, allow early clustering measurements, and provide a sample that is comparable in size to previous spectroscopic programs for studies of stellar, galaxy, and quasar physics, but to fainter magnitudes. The footprint of these observations can be found in Figure 8, and details of the targeted fields are given in Table 3.

The target selection algorithms for the One-Percent Survey were nearly the same as those for the 5 yr program, with only two minor modifications. First, the magnitude limit in the selection algorithm for the BGS Faint sample was increased to $r < 20.3$, rather than $r < 20.175$ as in the main survey. This led to an increase in the total surface density of the BGS Bright and the BGS Faint samples to $1,480 \text{ deg}^{-2}$ in the One-Percent Survey. Second, the selection algorithm for LRG targets was modified to be somewhat more inclusive in the One-Percent Survey. The faint limit was moved 0.1 mag fainter in $z_{\text{fiber}}$, and the sliding cut in $r$-W1 versus W1 was moved to include slightly fainter galaxies. The color-color cut in $g - r$ versus $r$-W1 was also shifted toward slightly bluer colors to increase the number density of lower-redshift galaxies.

The observations for the One-Percent Survey were conducted in nearly the same mode as expected for the 5 yr program. The summary of observations can be found in Table 1.

LRG, ELG, and quasar targets were observed during the times when sky background, seeing, and transparency were most conducive to spectroscopy of faint sources. In most cases, these targets were observed using the automated field selection when conditions indicated at least a 40% survey speed. To achieve the goal of very high completeness in all target classes, the tiling pattern followed a rosette pattern over 20 unique field centers. Each rosette consisted of at least 12 individual tiles offset by 0.12° from the field center. A minimum of 11 these tiles were observed for each rosette. Targets within a $7.0 \text{ deg}^2$ annulus had significant coverage, while those targets over an additional $2 \text{ deg}^2$ were observed with fewer visits and lower completeness in fiber assignment. Up to three additional visits were given to targets that produced spectra without secure redshift estimates. These additional visits were assigned only if there were no unobserved LRG, ELG, or quasar targets competing for the fiber. Over the regions between 0.2° and 1.45° from the field center, spectra were successfully obtained for 99% of LRG targets, 95% of ELG targets, and nearly 100% of quasar targets. The completeness statistics for each field are found in Table 3, and the completeness as a function of pairwise separation is presented in Figure 9. At such a high completeness in fiber assignment, the primary LRG sample for the main survey is nearly fully covered, even with the extensions described above.

BGS and MWS targets were observed during the times with slightly degraded conditions, where good signal-to-noise would still be achieved due to the higher source fluxes. In some cases, BGS and MWS tiles were observed during conditions that would have otherwise been considered for LRG, ELG, quasar observations because we needed the tiles to fill the observing queue for the entire night. The same rosette pattern was used for these targets, but with a minimum of 10 to be observed for each field. Spectroscopy was obtained for 99% for BGS Bright and for BGS Faint, and 96% for MWS targets. As with the
<table><caption>**Table 3**
List of Fields Included in the One-Percent Survey</caption><thead><tr><th rowspan="2">Field</th><th colspan="2">Field Center</th><th rowspan="2">MWS Completeness</th><th rowspan="2">BGS Completeness</th><th rowspan="2">LRG Completeness</th><th rowspan="2">ELG Completeness</th><th rowspan="2">Quasar Completeness</th></tr><tr><th>α (deg)</th><th>δ (deg)</th></tr></thead><tbody><tr><td>COSMOS</td><td>150.10</td><td>2.18</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.95</td><td>0.99</td></tr><tr><td>GAMA G12 #1</td><td>179.60</td><td>0.00</td><td>0.97</td><td>0.99</td><td>0.99</td><td>0.97</td><td>0.99</td></tr><tr><td>GAMA G12 #2</td><td>183.10</td><td>0.00</td><td>0.98</td><td>1.00</td><td>0.99</td><td>0.96</td><td>1.00</td></tr><tr><td>GOODS-North</td><td>189.90</td><td>61.80</td><td>0.98</td><td>0.99</td><td>0.99</td><td>0.98</td><td>1.00</td></tr><tr><td>Coma cluster</td><td>194.75</td><td>28.20</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>Coma outskirts</td><td>194.75</td><td>24.70</td><td>0.98</td><td>0.99</td><td>0.99</td><td>0.95</td><td>1.00</td></tr><tr><td>VVDS-F14</td><td>210.00</td><td>5.00</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.95</td><td>1.00</td></tr><tr><td>GAMA G15 #4</td><td>212.80</td><td>-0.60</td><td>0.94</td><td>0.98</td><td>0.99</td><td>0.93</td><td>1.00</td></tr><tr><td>DEEP2 CFHTLS-D3/W3</td><td>215.50</td><td>52.50</td><td>0.99</td><td>1.00</td><td>0.98</td><td>0.96</td><td>0.99</td></tr><tr><td>GAMA G15 #1</td><td>216.30</td><td>-0.60</td><td>0.96</td><td>0.99</td><td>0.98</td><td>0.93</td><td>0.99</td></tr><tr><td>Bootes</td><td>217.80</td><td>34.40</td><td>0.97</td><td>0.99</td><td>0.99</td><td>0.96</td><td>0.99</td></tr><tr><td>NDWFS/AGES</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GAMA G15 #3</td><td>218.05</td><td>2.43</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.94</td><td>1.00</td></tr><tr><td>GAMA G15 #2</td><td>219.80</td><td>-0.60</td><td>0.96</td><td>0.99</td><td>0.98</td><td>0.93</td><td>0.99</td></tr><tr><td>HSC DR2</td><td>236.10</td><td>43.45</td><td>0.99</td><td>1.00</td><td>0.98</td><td>0.94</td><td>1.00</td></tr><tr><td>HSC DR2 #1</td><td>241.05</td><td>43.45</td><td>0.98</td><td>0.99</td><td>0.97</td><td>0.95</td><td>0.97</td></tr><tr><td>ELAIS N1</td><td>242.75</td><td>54.98</td><td>0.93</td><td>0.98</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>HSC DR2 #2</td><td>245.88</td><td>43.45</td><td>0.95</td><td>0.99</td><td>0.98</td><td>0.95</td><td>1.00</td></tr><tr><td>XDEEP2</td><td>252.50</td><td>34.50</td><td>0.95</td><td>0.99</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>Euclid Deep Field</td><td>269.73</td><td>66.02</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>Near ecliptic pole</td><td>269.73</td><td>62.52</td><td>0.95</td><td>0.99</td><td>0.97</td><td>0.95</td><td>1.00</td></tr><tr><td>Average</td><td></td><td></td><td>0.962</td><td>0.989</td><td>0.986</td><td>0.952</td><td>0.994</td></tr></tbody></table>

**Note.** Completeness values correspond to the fraction of targets that received a valid observation within each target class. Completeness is computed using all targets that lie a distance 0.2–1.45 from the field center.

<figure><img src="image_12.png" /><figcaption>**Figure 9.** The completeness for pairs of targets in the One-Percent Survey as a function of angular separation. Pairs found in the regions that lie between 0.2 and 1.45 from each rosette field center are shown with solid lines, demonstrating the areas of highest completeness. Completeness of pairs with no cut on the distance to the rosette centers is in dashed lines. The pairwise completeness will be lower for the main survey when fewer tiles are dedicated to each coordinate on the sky.</figcaption></figure>

LRG program, the extension to fainter magnitudes had little impact on the fiber assignment completeness for the BGS Faint sample. Following the same strategy as above, additional fibers were given to targets that did not produce robust spectral classifications, with final statistics for all fields found in Table 3.

<caption>**Table 4**</caption>

Sample Sizes for Each Target Class in the 1 Month DESI One-Percent Survey Compared to Related Spectroscopic Samples (Driver et al. 2009; Dawson et al. 2016)

<table><thead><tr><th>Target Type</th><th>GAMA (k)</th><th>eBOSS (k)</th><th>DESI One-Percent Survey (k)</th></tr></thead><tbody><tr><td>LRG</td><td></td><td>232</td><td>139</td></tr><tr><td>ELG</td><td></td><td>223</td><td>298</td></tr><tr><td>QSO</td><td></td><td>545</td><td>38</td></tr><tr><td>BGS</td><td>150</td><td></td><td>252</td></tr><tr><td>MWS</td><td></td><td></td><td>212</td></tr></tbody></table>

**Note.** We report here the number of observed, secure redshifts. For DESI, we use the criteria described in Section 5, except for MWS where we simply use ZWARN = 0, and SPECTYPE = STAR.

Unlike the target selection validation program, the information from the guide cameras and sky monitors was used to compute the exposure times. Following the definition of effective exposure times in Section 3, the exposures of LRG, ELG, and quasar targets were taken to an equivalent of 1200 s, a factor 1.2 longer than the design for the main program. Exposure times of BGS and MWS targets were also increased by a factor of 1.2. The increased exposure time provided a margin against lingering uncertainties in calibration and real-time estimates of accumulated signal-to-noise.

In total, the One-Percent Survey produced 939,000 secure spectral classifications in only 1 month. The summary over all target classes compared to other major spectroscopic programs can be found in Table 4. In comparing to eBOSS, we use only data from the One-Percent dark time program. DESI observed
<table><caption>**Table 3**
List of Fields Included in the One-Percent Survey</caption><thead><tr><th rowspan="2">Field</th><th colspan="2">Field Center</th><th rowspan="2">MWS Completeness</th><th rowspan="2">BGS Completeness</th><th rowspan="2">LRG Completeness</th><th rowspan="2">ELG Completeness</th><th rowspan="2">Quasar Completeness</th></tr><tr><th>α (deg)</th><th>δ (deg)</th></tr></thead><tbody><tr><td>COSMOS</td><td>150.10</td><td>2.18</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.95</td><td>0.99</td></tr><tr><td>GAMA G12 #1</td><td>179.60</td><td>0.00</td><td>0.97</td><td>0.99</td><td>0.99</td><td>0.97</td><td>0.99</td></tr><tr><td>GAMA G12 #2</td><td>183.10</td><td>0.00</td><td>0.98</td><td>1.00</td><td>0.99</td><td>0.96</td><td>1.00</td></tr><tr><td>GOODS-North</td><td>189.90</td><td>61.80</td><td>0.98</td><td>0.99</td><td>0.99</td><td>0.98</td><td>1.00</td></tr><tr><td>Coma cluster</td><td>194.75</td><td>28.20</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>Coma outskirts</td><td>194.75</td><td>24.70</td><td>0.98</td><td>0.99</td><td>0.99</td><td>0.95</td><td>1.00</td></tr><tr><td>VVDS-F14</td><td>210.00</td><td>5.00</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.95</td><td>1.00</td></tr><tr><td>GAMA G15 #4</td><td>212.80</td><td>-0.60</td><td>0.94</td><td>0.98</td><td>0.99</td><td>0.93</td><td>1.00</td></tr><tr><td>DEEP2 CFHTLS-D3/W3</td><td>215.50</td><td>52.50</td><td>0.99</td><td>1.00</td><td>0.98</td><td>0.96</td><td>0.99</td></tr><tr><td>GAMA G15 #1</td><td>216.30</td><td>-0.60</td><td>0.96</td><td>0.99</td><td>0.98</td><td>0.93</td><td>0.99</td></tr><tr><td>Bootes</td><td>217.80</td><td>34.40</td><td>0.97</td><td>0.99</td><td>0.99</td><td>0.96</td><td>0.99</td></tr><tr><td>NDWFS/AGES</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GAMA G15 #3</td><td>218.05</td><td>2.43</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.94</td><td>1.00</td></tr><tr><td>GAMA G15 #2</td><td>219.80</td><td>-0.60</td><td>0.96</td><td>0.99</td><td>0.98</td><td>0.93</td><td>0.99</td></tr><tr><td>HSC DR2</td><td>236.10</td><td>43.45</td><td>0.99</td><td>1.00</td><td>0.98</td><td>0.94</td><td>1.00</td></tr><tr><td>HSC DR2 #1</td><td>241.05</td><td>43.45</td><td>0.98</td><td>0.99</td><td>0.97</td><td>0.95</td><td>0.97</td></tr><tr><td>ELAIS N1</td><td>242.75</td><td>54.98</td><td>0.93</td><td>0.98</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>HSC DR2 #2</td><td>245.88</td><td>43.45</td><td>0.95</td><td>0.99</td><td>0.98</td><td>0.95</td><td>1.00</td></tr><tr><td>XDEEP2</td><td>252.50</td><td>34.50</td><td>0.95</td><td>0.99</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>Euclid Deep Field</td><td>269.73</td><td>66.02</td><td>0.96</td><td>0.99</td><td>0.99</td><td>0.97</td><td>1.00</td></tr><tr><td>Near ecliptic pole</td><td>269.73</td><td>62.52</td><td>0.95</td><td>0.99</td><td>0.97</td><td>0.95</td><td>1.00</td></tr><tr><td>Average</td><td></td><td></td><td>0.962</td><td>0.989</td><td>0.986</td><td>0.952</td><td>0.994</td></tr></tbody></table>

**Note.** Completeness values correspond to the fraction of targets that received a valid observation within each target class. Completeness is computed using all targets that lie a distance 0.2–1.45 from the field center.

<figure><img src="image_13.png" /><figcaption>**Figure 9.** The completeness for pairs of targets in the One-Percent Survey as a function of angular separation. Pairs found in the regions that lie between 0.2 and 1.45 from each rosette field center are shown with solid lines, demonstrating the areas of highest completeness. Completeness of pairs with no cut on the distance to the rosette centers is in dashed lines. The pairwise completeness will be lower for the main survey when fewer tiles are dedicated to each coordinate on the sky.</figcaption></figure>

LRG program, the extension to fainter magnitudes had little impact on the fiber assignment completeness for the BGS Faint sample. Following the same strategy as above, additional fibers were given to targets that did not produce robust spectral classifications, with final statistics for all fields found in Table 3.

<caption>**Table 4**</caption>

Sample Sizes for Each Target Class in the 1 Month DESI One-Percent Survey Compared to Related Spectroscopic Samples (Driver et al. 2009; Dawson et al. 2016)

<table><thead><tr><th>Target Type</th><th>GAMA (k)</th><th>eBOSS (k)</th><th>DESI One-Percent Survey (k)</th></tr></thead><tbody><tr><td>LRG</td><td></td><td>232</td><td>139</td></tr><tr><td>ELG</td><td></td><td>223</td><td>298</td></tr><tr><td>QSO</td><td></td><td>545</td><td>38</td></tr><tr><td>BGS</td><td>150</td><td></td><td>252</td></tr><tr><td>MWS</td><td></td><td></td><td>212</td></tr></tbody></table>

**Note.** We report here the number of observed, secure redshifts. For DESI, we use the criteria described in Section 5, except for MWS where we simply use ZWARN = 0, and SPECTYPE = STAR.

Unlike the target selection validation program, the information from the guide cameras and sky monitors was used to compute the exposure times. Following the definition of effective exposure times in Section 3, the exposures of LRG, ELG, and quasar targets were taken to an equivalent of 1200 s, a factor 1.2 longer than the design for the main program. Exposure times of BGS and MWS targets were also increased by a factor of 1.2. The increased exposure time provided a margin against lingering uncertainties in calibration and real-time estimates of accumulated signal-to-noise.

In total, the One-Percent Survey produced 939,000 secure spectral classifications in only 1 month. The summary over all target classes compared to other major spectroscopic programs can be found in Table 4. In comparing to eBOSS, we use only data from the One-Percent dark time program. DESI observed
about half of the number of targets, but required a factor of 38 less exposure time.

## 5. Results

Following the reductions of the SV data, the one-dimensional spectra were modeled as a function of redshift and spectral type. The modeling software for this classification is named “Redrock” (S.J. Bailey et al. 2023, in preparation)<fnref n="113" /> and follows a procedure similar to BOSS spectral characterization (Bolton et al. 2012). Redrock is run on all spectra, but in this section, we ignore the statistics for those spectra that were assigned a flag corresponding to a failed spectrum in the data reductions.

The primary methodology within Redrock is a $\chi^2$ minimization computed from a linear combination of spectral templates over all trial redshifts. A suite of stellar, galaxy, and quasar templates is fit to each spectrum over a unique redshift range appropriate to each spectral class. The linear combination that gives the best fit to the data over all redshifts is assumed to be the best model. The key parameters describing the best fit are the redshift, the redshift uncertainty, the spectral class (star, galaxy, or quasar), the coefficients to the spectral templates, the $\chi^2$, and the value $\Delta\chi^2$. The parameter $\Delta\chi^2$ is defined as the difference in $\chi^2$ between the fit at the most likely redshift and the fit at the secondary minima in the $\chi^2$ function that denotes the second-best fit to the data. $\Delta\chi^2$ therefore characterizes the likelihood that the best-fit redshift is correct, with higher values of $\Delta\chi^2$ reflecting an increased probability that the estimate is correct.

Visual inspections of galaxy spectra (Lan et al. 2023) and quasar spectra (Alexander et al. 2023) were used to provide a first estimate of Redrock performance. These visual inspections were performed on composite spectra using all available exposures in the deepest fields in Table 1. Because the effective exposure times for these fields were roughly 10 times longer than planned in the initial survey design, visual inspectors were able to classify spectra at high confidence relative to the main survey, identify sources of spurious signal, and find common failure modes in the Redrock modeling. The feedback on spurious signal informed improvements to the data reduction algorithms in successive internal releases. In finding common failure modes in the Redrock modeling, the visual inspection process also allowed the DESI collaboration to customize algorithms for reliable spectral classification to each target class.

Once an algorithm was defined for determining whether a redshift was reliable, we used the spectra in the target selection validation data sample to empirically determine the quality of redshift estimates. In all cases, we subsampled the spectra to have effective exposure times of roughly 180 s for BGS and MWS targets and 1000 s for LRG, ELG, and quasar targets. With these data splits, we quantified the following for each target sample:

1. the total redshift efficiency, which is simply the fraction of spectra that produce a reliable redshift;

2. the target redshift efficiency, which is the fraction of spectra that produce a reliable redshift in the desired redshift range;

3. the catastrophic failure rate, which is the fraction of targets assigned an incorrect redshift; and

4. the statistical precision of the redshift estimates.

Catastrophic failure rates and redshift precision were computed using either pairs of repeated spectra, or individual exposures relative to a much deeper reference exposure. For those spectra that are assigned a reliable redshift in the desired redshift range, the catastrophic failure rate is defined as the fraction of spectra that produce a pairwise velocity difference exceeding 1000 km s⁻¹ for galaxies and 3000 km s⁻¹ for quasars. In this computation using pairs of repeated spectra, we implicitly assume that one redshift in the pair is correct, so the catastrophic failure rate is equal to half the fraction of pairs that produce discrepant redshifts. When using deeper spectra as a reference, we implicitly assume that the redshift in the higher-quality spectrum is correct. Where possible, we used redshift estimates from other surveys to assess the systematic errors in these redshift estimates.

In what follows, we describe the custom algorithm for determining the redshift of each target class. Using the target selection validation sample, we report the statistics regarding total redshift efficiency, target redshift efficiency, catastrophic failure rate, and statistical redshift precision for each sample. These statistics are reported in the other papers associated with the target selection validation, particularly those that describe the visual inspection process (Alexander et al. 2023; Lan et al. 2023). Occasional differences in the reported values are due to different assumptions in the samples. We then use the custom algorithms for each target class to summarize redshift completeness as a function of exposure time, thus setting the conditions for the exposure sequence in the main survey. We conclude with a summary of the performance on all spectroscopic samples compared to the requirements that drove the instrument design as described in DESI Collaboration et al. (2022). The results are found in Tables 5 and 6.

### 5.1. Redshift Determination

#### 5.1.1. Milky Way Survey (MWS)

Beyond the Redrock classification of stellar spectra and radial velocities, several MWS measurements (including radial velocities, stellar parameters, and chemical abundances) will be obtained by running additional template-fitting codes specialized for stellar spectra. As described in Cooper et al. (2023), two of these codes are developed for all stars while one is specific to white dwarfs. These additional algorithms will be run on all MWS targets (regardless of their classification by Redrock) and on any other sources that are classified as stars by Redrock. Here, we show results from the RVSpecfit (Koposov et al. 2011; Koposov 2019) code, which performs least-square fitting of stellar DESI spectra by interpolating between spectral templates to obtain radial (line-of-sight) velocities and stellar parameters.

The radial velocity precision of stars based on fits with RVSpecfit is illustrated in Figure 10. Only individual exposures are included with effective exposure times ranging from 100 to 300 s to sample the expected exposure times in the full MWS survey. The mean velocity measured from deep stacked exposures with effective exposure time larger than 1000 s is subtracted from each individual measurement to capture the statistical errors in each measurement. We then use the residuals in bins of color and magnitude to compute the

<footnote n="113">¹¹³ https://github.com/desihub/redrock/releases/tag/0.15.4</footnote>
about half of the number of targets, but required a factor of 38 less exposure time.

## 5. Results

Following the reductions of the SV data, the one-dimensional spectra were modeled as a function of redshift and spectral type. The modeling software for this classification is named “Redrock” (S.J. Bailey et al. 2023, in preparation)<fnref n="113" /> and follows a procedure similar to BOSS spectral characterization (Bolton et al. 2012). Redrock is run on all spectra, but in this section, we ignore the statistics for those spectra that were assigned a flag corresponding to a failed spectrum in the data reductions.

The primary methodology within Redrock is a $\chi^2$ minimization computed from a linear combination of spectral templates over all trial redshifts. A suite of stellar, galaxy, and quasar templates is fit to each spectrum over a unique redshift range appropriate to each spectral class. The linear combination that gives the best fit to the data over all redshifts is assumed to be the best model. The key parameters describing the best fit are the redshift, the redshift uncertainty, the spectral class (star, galaxy, or quasar), the coefficients to the spectral templates, the $\chi^2$, and the value $\Delta\chi^2$. The parameter $\Delta\chi^2$ is defined as the difference in $\chi^2$ between the fit at the most likely redshift and the fit at the secondary minima in the $\chi^2$ function that denotes the second-best fit to the data. $\Delta\chi^2$ therefore characterizes the likelihood that the best-fit redshift is correct, with higher values of $\Delta\chi^2$ reflecting an increased probability that the estimate is correct.

Visual inspections of galaxy spectra (Lan et al. 2023) and quasar spectra (Alexander et al. 2023) were used to provide a first estimate of Redrock performance. These visual inspections were performed on composite spectra using all available exposures in the deepest fields in Table 1. Because the effective exposure times for these fields were roughly 10 times longer than planned in the initial survey design, visual inspectors were able to classify spectra at high confidence relative to the main survey, identify sources of spurious signal, and find common failure modes in the Redrock modeling. The feedback on spurious signal informed improvements to the data reduction algorithms in successive internal releases. In finding common failure modes in the Redrock modeling, the visual inspection process also allowed the DESI collaboration to customize algorithms for reliable spectral classification to each target class.

Once an algorithm was defined for determining whether a redshift was reliable, we used the spectra in the target selection validation data sample to empirically determine the quality of redshift estimates. In all cases, we subsampled the spectra to have effective exposure times of roughly 180 s for BGS and MWS targets and 1000 s for LRG, ELG, and quasar targets. With these data splits, we quantified the following for each target sample:

1. the total redshift efficiency, which is simply the fraction of spectra that produce a reliable redshift;

2. the target redshift efficiency, which is the fraction of spectra that produce a reliable redshift in the desired redshift range;

3. the catastrophic failure rate, which is the fraction of targets assigned an incorrect redshift; and

4. the statistical precision of the redshift estimates.

Catastrophic failure rates and redshift precision were computed using either pairs of repeated spectra, or individual exposures relative to a much deeper reference exposure. For those spectra that are assigned a reliable redshift in the desired redshift range, the catastrophic failure rate is defined as the fraction of spectra that produce a pairwise velocity difference exceeding 1000 km s⁻¹ for galaxies and 3000 km s⁻¹ for quasars. In this computation using pairs of repeated spectra, we implicitly assume that one redshift in the pair is correct, so the catastrophic failure rate is equal to half the fraction of pairs that produce discrepant redshifts. When using deeper spectra as a reference, we implicitly assume that the redshift in the higher-quality spectrum is correct. Where possible, we used redshift estimates from other surveys to assess the systematic errors in these redshift estimates.

In what follows, we describe the custom algorithm for determining the redshift of each target class. Using the target selection validation sample, we report the statistics regarding total redshift efficiency, target redshift efficiency, catastrophic failure rate, and statistical redshift precision for each sample. These statistics are reported in the other papers associated with the target selection validation, particularly those that describe the visual inspection process (Alexander et al. 2023; Lan et al. 2023). Occasional differences in the reported values are due to different assumptions in the samples. We then use the custom algorithms for each target class to summarize redshift completeness as a function of exposure time, thus setting the conditions for the exposure sequence in the main survey. We conclude with a summary of the performance on all spectroscopic samples compared to the requirements that drove the instrument design as described in DESI Collaboration et al. (2022). The results are found in Tables 5 and 6.

### 5.1. Redshift Determination

#### 5.1.1. Milky Way Survey (MWS)

Beyond the Redrock classification of stellar spectra and radial velocities, several MWS measurements (including radial velocities, stellar parameters, and chemical abundances) will be obtained by running additional template-fitting codes specialized for stellar spectra. As described in Cooper et al. (2023), two of these codes are developed for all stars while one is specific to white dwarfs. These additional algorithms will be run on all MWS targets (regardless of their classification by Redrock) and on any other sources that are classified as stars by Redrock. Here, we show results from the RVSpecfit (Koposov et al. 2011; Koposov 2019) code, which performs least-square fitting of stellar DESI spectra by interpolating between spectral templates to obtain radial (line-of-sight) velocities and stellar parameters.

The radial velocity precision of stars based on fits with RVSpecfit is illustrated in Figure 10. Only individual exposures are included with effective exposure times ranging from 100 to 300 s to sample the expected exposure times in the full MWS survey. The mean velocity measured from deep stacked exposures with effective exposure time larger than 1000 s is subtracted from each individual measurement to capture the statistical errors in each measurement. We then use the residuals in bins of color and magnitude to compute the

<footnote n="113">¹¹³ https://github.com/desihub/redrock/releases/tag/0.15.4</footnote>
<table><caption>**Table 5**
Requirements and Performance for LRG, ELG, and Quasar Spectroscopy</caption><thead><tr><th>No.</th><th>Requirement</th><th>Performance</th></tr></thead><tbody><tr><td>L2</td><td>Survey Data Set Requirements</td><td></td></tr><tr><td>L2.2</td><td>Luminous Red Galaxies</td><td></td></tr><tr><td>L2.2.1</td><td>The average density with redshift 0.4 &lt; z &lt; 1.0 shall be at least 300 deg<sup>-2</sup>.</td><td>The average density with redshift 0.4 &lt; z &lt; 1.1 is 478 deg<sup>-2</sup>.</td></tr><tr><td>L2.2.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0005(1 + z).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.00014(1 + z).</td></tr><tr><td>L2.2.3</td><td>The systematic in the mean redshift shall be less than Δz = 0.0002(1 + z).</td><td>The systematic error in the mean redshift is Δz = 0.00001(1 + z).</td></tr><tr><td>L2.2.4</td><td>The catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> shall be &lt;5%.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 0.2%.</td></tr><tr><td>L2.2.5</td><td>The redshift completeness shall be &gt;95% for each pointing averaged over all fibers with targets.</td><td>The fraction of targets confirmed as galaxies is 96% over all fibers that receive targets.</td></tr><tr><td>L2.3</td><td>Emission Line Galaxies</td><td></td></tr><tr><td>L2.3.1</td><td>The average density with redshift 0.6 &lt; z &lt; 1.6 shall be at least 1280 deg<sup>-2</sup>.</td><td>The average density of ELG_LOP targets with redshift 0.6 &lt; z &lt; 1.6 is 860 deg<sup>-2</sup>.</td></tr><tr><td>L2.3.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0005(1 + z).</td><td>The average density of ELG_VLO targets with redshift 0.6 &lt; z &lt; 1.6 is 180 deg<sup>-2</sup>.</td></tr><tr><td>L2.3.3</td><td>The systematic in the mean redshift shall be less than Δz = 0.0002(1 + z).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.000026(1 + z).</td></tr><tr><td>L2.3.4</td><td>The catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> shall be &lt;5%.</td><td>The typical systematic error in the mean redshift is σ<sub>z</sub> = 0.0000033(1 + z).</td></tr><tr><td>L2.3.5</td><td>The redshift completeness shall be &gt;90% for each pointing averaged over all targets above the O II flux limit.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 0.2%.</td></tr><tr><td>L2.4</td><td>Tracer Quasars (0.9 &lt; z &lt; 2.1)</td><td>The redshift completeness over all fibers with targets is ~70% for the ELG_LOP and ~94% for the ELG_VLO.</td></tr><tr><td>L2.4.1</td><td>The average density with redshift z &lt; 2.1 shall be at least 120 deg<sup>-2</sup>.</td><td>The average density with redshift z &lt; 2.1 is 144 deg<sup>-2</sup>.</td></tr><tr><td>L2.4.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0025(1 + z) (equivalent to 750 km s<sup>-1</sup> rms).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.00041(1 + z).</td></tr><tr><td>L2.4.3</td><td>The systematic in the mean redshift shall be less than Δz = 0.0004(1 + z).</td><td>The typical systematic error in the mean redshift is σ<sub>z</sub> = 0.000087(1 + z).</td></tr><tr><td>L2.4.4</td><td>The catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> shall be &lt;5%.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 4.8%.</td></tr><tr><td>L2.4.5</td><td>The redshift completeness shall be &gt;90% for each pointing averaged over all fibers with targets.</td><td>The redshift completeness of confirmed quasars is 66% (total completeness not recorded).</td></tr><tr><td>L2.5</td><td>Ly-α Quasars</td><td></td></tr><tr><td>L2.5.1</td><td>The average density with redshift z &gt; 2.1 and r &lt; 23.5 mag shall be at least 50 deg<sup>-2</sup>.</td><td>The average density with redshift z &gt; 2.1 and r &lt; 23.0 mag is 58.5 deg<sup>-2</sup>.</td></tr><tr><td>L2.5.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0025(1 + z) (equivalent to 750 km s<sup>-1</sup> rms).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.00027(1 + z).</td></tr><tr><td>L2.5.3</td><td>The catastrophic redshift failures shall be &lt;2%.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 12.2%. The rate of catastrophic redshift failures exceeding 3000 km s<sup>-1</sup> is 1.8%.</td></tr><tr><td>L2.5.4</td><td>The S/N per Angstrom (observer frame) shall be greater than 1 in the Lyα forest for g = 23 mag and scale with flux for brighter quasars.</td><td>To be determined.</td></tr></tbody></table>

standard deviation as estimated from the difference between the 84th and 16th percentiles. The RV precision determined in this way is somewhat worse than the formal uncertainty returned from spectral fitting due to additional velocity systematic errors likely associated with wavelength calibration at the level of ~1 km s<sup>-1</sup> (see further discussion in Cooper et al. 2023; Guy et al. 2023). Using the measurements with radial velocity deviating from the value measured from the stack by more than 20 km s<sup>-1</sup>, the fraction of catastrophic errors is 0.6% for stars in the color-magnitude range of the MWS survey 0 &lt; g - r &lt; 2 and 16 &lt; r &lt; 19. Some fraction of these may be due to stars with binary motions.

### 5.1.2. Bright Galaxy Survey (BGS)

The BGS sample is largely magnitude limited and thus tuned for lower redshifts than the LRG, ELG, or quasar samples. The

redshift range 0 &lt; z &lt; 0.4 is covered at very high density with minimal overlap (roughly 5%) with the other tracers. These redshifts are assumed as the target range for BGS clustering studies. Good redshifts for BGS galaxies are those that produce a Δχ<sup>2</sup> > 40, a spectral classification of galaxy, and a reported statistical redshift uncertainty less than 0.0005(1 + z). We report the performance of Redrock for both the BGS Bright and BGS Faint samples according to this definition for a reliable redshift. We find a high-redshift success rate for all magnitudes, with redshift completeness exceeding 95% even near the magnitude limits of the BGS Bright sample.

The velocity differences relative to deep coadds for BGS Bright and BGS Faint targets at redshifts z &lt; 0.4 are presented in the left and right panels of Figure 11, respectively. Because of its small size, we do not report statistics for the BGS AGN sample. We compared the redshift estimates from DESI to
<table><caption>**Table 5**
Requirements and Performance for LRG, ELG, and Quasar Spectroscopy</caption><thead><tr><th>No.</th><th>Requirement</th><th>Performance</th></tr></thead><tbody><tr><td>L2</td><td>Survey Data Set Requirements</td><td></td></tr><tr><td>L2.2</td><td>Luminous Red Galaxies</td><td></td></tr><tr><td>L2.2.1</td><td>The average density with redshift 0.4 &lt; z &lt; 1.0 shall be at least 300 deg<sup>-2</sup>.</td><td>The average density with redshift 0.4 &lt; z &lt; 1.1 is 478 deg<sup>-2</sup>.</td></tr><tr><td>L2.2.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0005(1 + z).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.00014(1 + z).</td></tr><tr><td>L2.2.3</td><td>The systematic in the mean redshift shall be less than Δz = 0.0002(1 + z).</td><td>The systematic error in the mean redshift is Δz = 0.00001(1 + z).</td></tr><tr><td>L2.2.4</td><td>The catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> shall be &lt;5%.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 0.2%.</td></tr><tr><td>L2.2.5</td><td>The redshift completeness shall be &gt;95% for each pointing averaged over all fibers with targets.</td><td>The fraction of targets confirmed as galaxies is 96% over all fibers that receive targets.</td></tr><tr><td>L2.3</td><td>Emission Line Galaxies</td><td></td></tr><tr><td>L2.3.1</td><td>The average density with redshift 0.6 &lt; z &lt; 1.6 shall be at least 1280 deg<sup>-2</sup>.</td><td>The average density of ELG_LOP targets with redshift 0.6 &lt; z &lt; 1.6 is 860 deg<sup>-2</sup>.</td></tr><tr><td>L2.3.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0005(1 + z).</td><td>The average density of ELG_VLO targets with redshift 0.6 &lt; z &lt; 1.6 is 180 deg<sup>-2</sup>.</td></tr><tr><td>L2.3.3</td><td>The systematic in the mean redshift shall be less than Δz = 0.0002(1 + z).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.000026(1 + z).</td></tr><tr><td>L2.3.4</td><td>The catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> shall be &lt;5%.</td><td>The typical systematic error in the mean redshift is σ<sub>z</sub> = 0.0000033(1 + z).</td></tr><tr><td>L2.3.5</td><td>The redshift completeness shall be &gt;90% for each pointing averaged over all targets above the O II flux limit.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 0.2%.</td></tr><tr><td>L2.4</td><td>Tracer Quasars (0.9 &lt; z &lt; 2.1)</td><td>The redshift completeness over all fibers with targets is ~70% for the ELG_LOP and ~94% for the ELG_VLO.</td></tr><tr><td>L2.4.1</td><td>The average density with redshift z &lt; 2.1 shall be at least 120 deg<sup>-2</sup>.</td><td>The average density with redshift z &lt; 2.1 is 144 deg<sup>-2</sup>.</td></tr><tr><td>L2.4.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0025(1 + z) (equivalent to 750 km s<sup>-1</sup> rms).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.00041(1 + z).</td></tr><tr><td>L2.4.3</td><td>The systematic in the mean redshift shall be less than Δz = 0.0004(1 + z).</td><td>The typical systematic error in the mean redshift is σ<sub>z</sub> = 0.000087(1 + z).</td></tr><tr><td>L2.4.4</td><td>The catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> shall be &lt;5%.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 4.8%.</td></tr><tr><td>L2.4.5</td><td>The redshift completeness shall be &gt;90% for each pointing averaged over all fibers with targets.</td><td>The redshift completeness of confirmed quasars is 66% (total completeness not recorded).</td></tr><tr><td>L2.5</td><td>Ly-α Quasars</td><td></td></tr><tr><td>L2.5.1</td><td>The average density with redshift z &gt; 2.1 and r &lt; 23.5 mag shall be at least 50 deg<sup>-2</sup>.</td><td>The average density with redshift z &gt; 2.1 and r &lt; 23.0 mag is 58.5 deg<sup>-2</sup>.</td></tr><tr><td>L2.5.2</td><td>The random redshift error shall be less than σ<sub>z</sub> = 0.0025(1 + z) (equivalent to 750 km s<sup>-1</sup> rms).</td><td>The typical random redshift error is σ<sub>z</sub> = 0.00027(1 + z).</td></tr><tr><td>L2.5.3</td><td>The catastrophic redshift failures shall be &lt;2%.</td><td>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is 12.2%. The rate of catastrophic redshift failures exceeding 3000 km s<sup>-1</sup> is 1.8%.</td></tr><tr><td>L2.5.4</td><td>The S/N per Angstrom (observer frame) shall be greater than 1 in the Lyα forest for g = 23 mag and scale with flux for brighter quasars.</td><td>To be determined.</td></tr></tbody></table>

standard deviation as estimated from the difference between the 84th and 16th percentiles. The RV precision determined in this way is somewhat worse than the formal uncertainty returned from spectral fitting due to additional velocity systematic errors likely associated with wavelength calibration at the level of ~1 km s<sup>-1</sup> (see further discussion in Cooper et al. 2023; Guy et al. 2023). Using the measurements with radial velocity deviating from the value measured from the stack by more than 20 km s<sup>-1</sup>, the fraction of catastrophic errors is 0.6% for stars in the color-magnitude range of the MWS survey 0 &lt; g - r &lt; 2 and 16 &lt; r &lt; 19. Some fraction of these may be due to stars with binary motions.

### 5.1.2. Bright Galaxy Survey (BGS)

The BGS sample is largely magnitude limited and thus tuned for lower redshifts than the LRG, ELG, or quasar samples. The

redshift range 0 &lt; z &lt; 0.4 is covered at very high density with minimal overlap (roughly 5%) with the other tracers. These redshifts are assumed as the target range for BGS clustering studies. Good redshifts for BGS galaxies are those that produce a Δχ<sup>2</sup> > 40, a spectral classification of galaxy, and a reported statistical redshift uncertainty less than 0.0005(1 + z). We report the performance of Redrock for both the BGS Bright and BGS Faint samples according to this definition for a reliable redshift. We find a high-redshift success rate for all magnitudes, with redshift completeness exceeding 95% even near the magnitude limits of the BGS Bright sample.

The velocity differences relative to deep coadds for BGS Bright and BGS Faint targets at redshifts z &lt; 0.4 are presented in the left and right panels of Figure 11, respectively. Because of its small size, we do not report statistics for the BGS AGN sample. We compared the redshift estimates from DESI to
<table><caption>**Table 6**
MWS Spectroscopy, BGS Spectroscopy, Calibration, Fiber Assignment, and Target Selection</caption><thead><tr><th>No.</th><th>Requirement</th><th>Performance</th></tr></thead><tbody><tr><td></td><td>Milky Way Survey</td><td>The typical (median) radial velocity uncertainty is approximately σ<sub>v</sub> = 1.3 km s<sup>-1</sup>.</td></tr><tr><td></td><td>Bright Galaxy Survey</td><td>The rate of catastrophic redshift failures exceeding 20 km s<sup>-1</sup> is approximately 0.6%.<br>The average density of confirmed BGS Bright galaxies with redshift 0 &lt; z &lt; 0.4 is 646 deg<sup>-2</sup>.<br>The typical random redshift error is σ<sub>z</sub> = 0.00003(1 + z).<br>The typical systematic in the mean redshift is σ<sub>z</sub> = 0.000022(1 + z).<br>The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is approximately 0.5%.<br>The redshift completeness is 99% over all fibers that receive targets.</td></tr><tr><td>L2.6</td><td>Spectrophotometric Calibration</td><td></td></tr><tr><td>L2.6.1</td><td>The Lyα QSO fractional flux calibration errors shall have power less than 1.2 km s<sup>-1</sup> at k ~ 0.001 s km<sup>-1</sup>.</td><td>To be determined.</td></tr><tr><td>L2.7</td><td>Fiber Completeness</td><td></td></tr><tr><td>L2.7.1</td><td>The fraction of targets that receive a fiber shall be at least 80%.</td><td>The fraction of LRG targets that successfully acquire a spectrum is 89%.<br>The fraction of ELG_LOP targets that successfully acquire a spectrum is 69%.<br>The fraction of quasar targets that successfully acquire a spectrum is 99%.<br>The fraction of BGS Bright targets that successfully acquire a spectrum is 80%.<br>The fraction of MWS targets that successfully acquire a spectrum is 28%.</td></tr><tr><td>L2.8</td><td>Target Selection</td><td></td></tr><tr><td>L2.8.1</td><td>The LRG target density shall be 350 deg<sup>-2</sup>, with at least 300 deg<sup>-2</sup> successfully measured.</td><td>The LRG target density is 624 deg<sup>-2</sup>, with 533 deg<sup>-2</sup> successfully measured.</td></tr><tr><td>L2.8.2</td><td>The ELG target density shall be 2400 deg<sup>-2</sup>, with at least 1280 deg<sup>-2</sup> successfully measured.</td><td>The ELG_LOP target density is 1941 deg<sup>-2</sup>, with 938 deg<sup>-2</sup> successfully measured.<br>The ELG_VLO target density is 463 deg<sup>-2</sup>, with 183 deg<sup>-2</sup> successfully measured.</td></tr><tr><td>L2.8.3</td><td>The low-z QSO target density shall be 170 deg<sup>-2</sup>, with at least 120 deg<sup>-2</sup> successfully measured.</td><td>The quasar target density is 311 deg<sup>-2</sup>, with 144 deg<sup>-2</sup> successfully measured at z &lt; 2.1.</td></tr><tr><td>L2.8.4</td><td>The Lyα QSO target density shall be 90 deg<sup>-2</sup>, with at least 50 deg<sup>-2</sup> successfully measured.</td><td>58.5 deg<sup>-2</sup> quasars at z &gt; 2.1 are successfully measured from the overall quasar target sample.<br>The BGS Bright target density is 854 deg<sup>-2</sup>, with 676 deg<sup>-2</sup> successfully measured.<br>The density of MWS targets (excluding the Faint samples) is 1637 deg<sup>-2</sup>, with 458 deg<sup>-2</sup> successfully measured.</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Figure 10.** The precision of radial velocity estimates from the stellar radial velocity pipeline as a function of color and magnitude. The precision is measured in each color–magnitude bin by determining the 68% confidence region in offsets between radial velocities from 100 to 300 s individual exposures and radial velocities measured from deep exposures.</figcaption></figure>

those from the DEEP2 survey (Newman et al. 2013) for objects in common between the two surveys. We find average systematic offsets of only 6.5 ± 1.7 km s<sup>-1</sup>.

### 5.1.3. Luminous Red Galaxies (LRG)

We use the redshifts 0.4 < z < 1.1 as the target range for the LRG sample. To reject incorrect redshifts, we require that observed LRG spectra meet the following quality cuts:

Δχ<sup>2</sup> > 15, z<sub>redrock</sub> < 1.5, and the redshift warning flag, ZWARN = 0. Here, the ZWARN flag is a bitwise output from Redrock that captures the quality of the model fit. A value of 0 indicates that there is no clear evidence for a corrupted redshift estimate. The quality cuts remove roughly 1.1% of the observed LRG targets. Based on comparison with deep observations, we estimate that roughly 0.2% of the LRGs that meet the quality cuts are catastrophic failures.

The preliminary algorithm for classifying spectra produces a total redshift efficiency of 98.9%, and a target redshift efficiency (i.e., LRGs in 0.4 < z < 1.1 with secure redshifts) of 89.4%. The pairwise velocity differences are presented in Figure 12.

To estimate the systematic errors in the LRG redshifts, we compare the DESI redshifts with redshifts of the same objects from SDSS, BOSS, eBOSS (Ross et al. 2020), and the DEEP2 Survey (Newman et al. 2013). We find average offsets of less than 10 km s<sup>-1</sup>.

### 5.1.4. Emission Line Galaxies (ELG)

The ELG_LOP targets were optimized for redshifts 1.1 < z < 1.6, while the ELG_VLO targets were optimized to cover the full redshift range 0.6 < z < 1.6. The lower-redshift, ELG_VLO sample produces a higher fraction of reliable classifications because there is more information from the continuum and additional emission lines. In what follows, we present results for both the ELG_LOP and ELG_VLO targets over the interval 0.6 < z < 1.6.
<table><caption>**Table 6**
MWS Spectroscopy, BGS Spectroscopy, Calibration, Fiber Assignment, and Target Selection</caption><thead><tr><th>No.</th><th>Requirement</th><th>Performance</th></tr></thead><tbody><tr><td></td><td>Milky Way Survey</td><td>The typical (median) radial velocity uncertainty is approximately σ<sub>v</sub> = 1.3 km s<sup>-1</sup>.</td></tr><tr><td></td><td>Bright Galaxy Survey</td><td>The rate of catastrophic redshift failures exceeding 20 km s<sup>-1</sup> is approximately 0.6%. The average density of confirmed BGS Bright galaxies with redshift 0 &lt; z &lt; 0.4 is 646 deg<sup>-2</sup>. The typical random redshift error is σ<sub>z</sub> = 0.00003(1 + z). The typical systematic in the mean redshift is σ<sub>z</sub> = 0.000022(1 + z). The rate of catastrophic redshift failures exceeding 1000 km s<sup>-1</sup> is approximately 0.5%. The redshift completeness is 99% over all fibers that receive targets.</td></tr><tr><td>L2.6</td><td>Spectrophotometric Calibration</td><td></td></tr><tr><td>L2.6.1</td><td>The Lyα QSO fractional flux calibration errors shall have power less than 1.2 km s<sup>-1</sup> at k ~ 0.001 s km<sup>-1</sup>.</td><td>To be determined.</td></tr><tr><td>L2.7</td><td>Fiber Completeness</td><td></td></tr><tr><td>L2.7.1</td><td>The fraction of targets that receive a fiber shall be at least 80%.</td><td>The fraction of LRG targets that successfully acquire a spectrum is 89%. The fraction of ELG_LOP targets that successfully acquire a spectrum is 69%. The fraction of quasar targets that successfully acquire a spectrum is 99%. The fraction of BGS Bright targets that successfully acquire a spectrum is 80%. The fraction of MWS targets that successfully acquire a spectrum is 28%.</td></tr><tr><td>L2.8</td><td>Target Selection</td><td></td></tr><tr><td>L2.8.1</td><td>The LRG target density shall be 350 deg<sup>-2</sup>, with at least 300 deg<sup>-2</sup> successfully measured.</td><td>The LRG target density is 624 deg<sup>-2</sup>, with 533 deg<sup>-2</sup> successfully measured.</td></tr><tr><td>L2.8.2</td><td>The ELG target density shall be 2400 deg<sup>-2</sup>, with at least 1280 deg<sup>-2</sup> successfully measured.</td><td>The ELG_LOP target density is 1941 deg<sup>-2</sup>, with 938 deg<sup>-2</sup> successfully measured. The ELG_VLO target density is 463 deg<sup>-2</sup>, with 183 deg<sup>-2</sup> successfully measured. The quasar target density is 311 deg<sup>-2</sup>, with 144 deg<sup>-2</sup> successfully measured at z &lt; 2.1.</td></tr><tr><td>L2.8.3</td><td>The low-z QSO target density shall be 170 deg<sup>-2</sup>, with at least 120 deg<sup>-2</sup> successfully measured.</td><td>58.5 deg<sup>-2</sup> quasars at z &gt; 2.1 are successfully measured from the overall quasar target sample.</td></tr><tr><td>L2.8.4</td><td>The Lyα QSO target density shall be 90 deg<sup>-2</sup>, with at least 50 deg<sup>-2</sup> successfully measured.</td><td>The BGS Bright target density is 854 deg<sup>-2</sup>, with 676 deg<sup>-2</sup> successfully measured. The density of MWS targets (excluding the Faint samples) is 1637 deg<sup>-2</sup>, with 458 deg<sup>-2</sup> successfully measured.</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>**Figure 10.** The precision of radial velocity estimates from the stellar radial velocity pipeline as a function of color and magnitude. The precision is measured in each color–magnitude bin by determining the 68% confidence region in offsets between radial velocities from 100 to 300 s individual exposures and radial velocities measured from deep exposures.</figcaption></figure>

those from the DEEP2 survey (Newman et al. 2013) for objects in common between the two surveys. We find average systematic offsets of only 6.5 ± 1.7 km s<sup>-1</sup>.

### 5.1.3. Luminous Red Galaxies (LRG)

We use the redshifts 0.4 < z < 1.1 as the target range for the LRG sample. To reject incorrect redshifts, we require that observed LRG spectra meet the following quality cuts:

Δχ<sup>2</sup> > 15, z<sub>redrock</sub> < 1.5, and the redshift warning flag, ZWARN = 0. Here, the ZWARN flag is a bitwise output from Redrock that captures the quality of the model fit. A value of 0 indicates that there is no clear evidence for a corrupted redshift estimate. The quality cuts remove roughly 1.1% of the observed LRG targets. Based on comparison with deep observations, we estimate that roughly 0.2% of the LRGs that meet the quality cuts are catastrophic failures.

The preliminary algorithm for classifying spectra produces a total redshift efficiency of 98.9%, and a target redshift efficiency (i.e., LRGs in 0.4 < z < 1.1 with secure redshifts) of 89.4%. The pairwise velocity differences are presented in Figure 12.

To estimate the systematic errors in the LRG redshifts, we compare the DESI redshifts with redshifts of the same objects from SDSS, BOSS, eBOSS (Ross et al. 2020), and the DEEP2 Survey (Newman et al. 2013). We find average offsets of less than 10 km s<sup>-1</sup>.

### 5.1.4. Emission Line Galaxies (ELG)

The ELG_LOP targets were optimized for redshifts 1.1 < z < 1.6, while the ELG_VLO targets were optimized to cover the full redshift range 0.6 < z < 1.6. The lower-redshift, ELG_VLO sample produces a higher fraction of reliable classifications because there is more information from the continuum and additional emission lines. In what follows, we present results for both the ELG_LOP and ELG_VLO targets over the interval 0.6 < z < 1.6.
<figure><img src="image_14.png" /><figcaption>**Figure 11.** The difference in redshift (kilometers per second) between individual observations and deep exposures of the same BGS target. The $\Delta\chi^2$ assigned to each data point is taken from the single epoch observation. Spectra are only included if they were characterized as having a good redshift at $z < 0.4$. The vertical line represents the threshold for the $\Delta\chi^2$ value of a good redshift while the horizontal line represents the limit at which a redshift discrepancy is considered a catastrophic failure. The left panel shows the distribution of pairs for the BGS Bright sample while the right panel shows the distribution for the BGS Faint sample.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 12.** The difference in redshift between pairs of observations of the same LRG target. The vertical line represents the $\Delta\chi^2 > 15$ threshold for an accepted redshift while the horizontal line represents the limit at which a redshift discrepancy is considered a catastrophic failure. The LRG redshift quality cuts also reject any object with $z > 1.5$, which causes some of the redshifts with $\Delta\chi^2 > 15$ to be rejected (red).</figcaption></figure>

The same criteria are used to assign reliable redshifts to both the ELG_LOP and ELG_VLO samples. Because the ELG spectra will be the faintest targets observed in DESI, the spectra typically yield flux measurements at a low S/N over the continuum, with high signal-to-noise measurements localized to the O II emission regions. However, the redshifts that are reliably estimated based on flux from the O II doublet may not have a large $\Delta\chi^2$ value because of the small number of pixels and the lack of meaningful information over the continuum. For this reason, we use the measurement S/N($F_{O\ II}$) in addition to $\Delta\chi^2$ for ELG redshift estimates reported here. S/N($F_{O\ II}$) is a measurement of the S/N of the O II flux customized to ELG

spectra. By applying a cut in the (S/N($F_{O\ II}$), $\Delta\chi^2$) plane, we can reliably estimate the redshift based on the O II doublet in cases where a low value of $\Delta\chi^2$ may otherwise indicate a poor redshift estimate. Specifically, we adopt the preliminary selection $\log_{10}(\text{SNR}(F_{O\ II})) > 0.9-0.2 \times \log_{10}(\Delta\chi^2)$ for determining whether a redshift estimate is reliable.

The preliminary algorithm for classifying spectra produces total redshift efficiencies of 70% and 95% for the ELG_LOP and ELG_VLO samples, respectively. The pairwise velocity differences for ELG_LOP (ELG_VLO) targets over the target redshift range are presented in the left panel (right panel) of Figure 13.

To estimate the systematic errors in redshift, we compare the results from individual galaxies that DESI observed in common with eBOSS (Raichoor et al. 2021) or the DEEP2 survey (Newman et al. 2013). In both cases, we find average offsets of only $1 \pm 0.4 \text{ km s}^{-1}$, indicating that the systematic errors are small enough to be ignored.

### 5.1.5. Quasars (QSO)

The quasars will have the largest redshift range of all samples in DESI, reaching redshifts $z > 5$. Previous BAO studies (e.g., Neveux et al. 2020; Hou et al. 2021) used quasars as discrete tracers over the redshift range $0.8 < z < 2.2$ while those using the Ly-$\alpha$ forest (du Mas des Bourboux et al. 2020) relied on quasars at redshifts $z > 2.1$. Although the redshift ranges for DESI cosmology studies are yet to be established, we report redshift performance statistics for quasar tracers over two independent redshift ranges for simplicity. We assume target redshift ranges of $0.9 < z < 2.1$ and $z \ge 2.1$ for discrete tracer and Ly-$\alpha$ forest quasars, respectively. Those spectra that are not classified as a quasar are not included in the statistics of redshift performance.

The visual inspection process indicated that the quasar selection produces spectra of which 71% are classified as quasar, 16% are classified as galaxy, and 6% are classified as star. Around 7% of visually inspected spectra did not produce a
<figure><img src="image_15.png" /><figcaption>**Figure 11.** The difference in redshift (kilometers per second) between individual observations and deep exposures of the same BGS target. The $\Delta\chi^2$ assigned to each data point is taken from the single epoch observation. Spectra are only included if they were characterized as having a good redshift at $z < 0.4$. The vertical line represents the threshold for the $\Delta\chi^2$ value of a good redshift while the horizontal line represents the limit at which a redshift discrepancy is considered a catastrophic failure. The left panel shows the distribution of pairs for the BGS Bright sample while the right panel shows the distribution for the BGS Faint sample.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Figure 12.** The difference in redshift between pairs of observations of the same LRG target. The vertical line represents the $\Delta\chi^2 > 15$ threshold for an accepted redshift while the horizontal line represents the limit at which a redshift discrepancy is considered a catastrophic failure. The LRG redshift quality cuts also reject any object with $z > 1.5$, which causes some of the redshifts with $\Delta\chi^2 > 15$ to be rejected (red).</figcaption></figure>

The same criteria are used to assign reliable redshifts to both the ELG_LOP and ELG_VLO samples. Because the ELG spectra will be the faintest targets observed in DESI, the spectra typically yield flux measurements at a low S/N over the continuum, with high signal-to-noise measurements localized to the O II emission regions. However, the redshifts that are reliably estimated based on flux from the O II doublet may not have a large $\Delta\chi^2$ value because of the small number of pixels and the lack of meaningful information over the continuum. For this reason, we use the measurement S/N($F_{O\ II}$) in addition to $\Delta\chi^2$ for ELG redshift estimates reported here. S/N($F_{O\ II}$) is a measurement of the S/N of the O II flux customized to ELG

spectra. By applying a cut in the (S/N($F_{O\ II}$), $\Delta\chi^2$) plane, we can reliably estimate the redshift based on the O II doublet in cases where a low value of $\Delta\chi^2$ may otherwise indicate a poor redshift estimate. Specifically, we adopt the preliminary selection $\log_{10}(\text{SNR}(F_{O\ II})) > 0.9-0.2 \times \log_{10}(\Delta\chi^2)$ for determining whether a redshift estimate is reliable.

The preliminary algorithm for classifying spectra produces total redshift efficiencies of 70% and 95% for the ELG_LOP and ELG_VLO samples, respectively. The pairwise velocity differences for ELG_LOP (ELG_VLO) targets over the target redshift range are presented in the left panel (right panel) of Figure 13.

To estimate the systematic errors in redshift, we compare the results from individual galaxies that DESI observed in common with eBOSS (Raichoor et al. 2021) or the DEEP2 survey (Newman et al. 2013). In both cases, we find average offsets of only $1 \pm 0.4 \text{ km s}^{-1}$, indicating that the systematic errors are small enough to be ignored.

### 5.1.5. Quasars (QSO)

The quasars will have the largest redshift range of all samples in DESI, reaching redshifts $z > 5$. Previous BAO studies (e.g., Neveux et al. 2020; Hou et al. 2021) used quasars as discrete tracers over the redshift range $0.8 < z < 2.2$ while those using the Ly-$\alpha$ forest (du Mas des Bourboux et al. 2020) relied on quasars at redshifts $z > 2.1$. Although the redshift ranges for DESI cosmology studies are yet to be established, we report redshift performance statistics for quasar tracers over two independent redshift ranges for simplicity. We assume target redshift ranges of $0.9 < z < 2.1$ and $z \ge 2.1$ for discrete tracer and Ly-$\alpha$ forest quasars, respectively. Those spectra that are not classified as a quasar are not included in the statistics of redshift performance.

The visual inspection process indicated that the quasar selection produces spectra of which 71% are classified as quasar, 16% are classified as galaxy, and 6% are classified as star. Around 7% of visually inspected spectra did not produce a
<figure><img src="image_16.png" /><figcaption>**Figure 13.** The difference in redshift (kilometers per second) between pairs of observations taken of the same ELG target. A linear combination of $log(S/N(F_{\text{O II}}))$ and $log(\Delta\chi^2)$ is used to determine whether a redshift is reliable. The vertical line represents the threshold for the preliminary value where we assume a good redshift estimate. The horizontal line represents the limit at which a redshift discrepancy is considered a catastrophic failure. Left: the distribution of pairs for the ELG\_LOP sample. Right: The distribution for the ELG\_VLO sample. In both panels, a measurement is only included if one spectrum in the pair was characterized as having a redshift estimate in the range $0.6 < z < 1.6$ and if both measurements of the pair have a valid estimate of $S/N(F_{\text{O II}})$ and $\Delta\chi^2$.</figcaption></figure>

conclusive classification or redshift. A large number of quasar spectra with broad emission lines were misclassified as galaxies by Redrock, often at the incorrect redshift. Based on this performance, we developed a method for automated classification based on Redrock estimates of redshift and classification with additional filtering from two customized algorithms. The first of these algorithms provides an estimate of Mg II flux while the second relies on a machine-learning classifier called QuasarNet (Busca & Balland 2018; Farr et al. 2020a).

The first application of these algorithms is designed to recover quasar spectra that were misclassified by Redrock. If a spectrum from the quasar sample is classified by Redrock as a galaxy, we first assess the fits of the Mg II emission line. If a line is detected with an equivalent width between 10 and 200 Å, a significance of at least three standard deviations, and an overall improvement to the fit of $\chi^2 > 16$, then we assume that the redshift estimate was correct and change the classification to that of a quasar. If no significant Mg II flux was detected, we then assess the output of QuasarNet to determine whether the spectrum is actually a quasar at a different redshift. If QuasarNet classifies the object as a quasar with a probability higher than 95%, we compute a new redshift based on the Redrock $\chi^2$ surface evaluated only over a narrow redshift interval ($\Delta z = 0.05$) centered on the QuasarNet redshift estimate.

The second application of these algorithms is designed to recover quasar redshifts that were estimated incorrectly by Redrock. This occurs when both Redrock and QuasarNet identify the object as a quasar but when the two redshifts differ by more than 0.05. Then, as before, we recalculate a new redshift based on the Redrock $\chi^2$ surface evaluated only over a narrow redshift interval ($\Delta z = 0.05$) centered on the QuasarNet redshift estimate.

If either of the conditions described above is satisfied, the spectrum is included in the catalog. In cases where the classification of quasars is not based on the first estimate from Redrock, the value of $\Delta\chi^2$ for the final estimate is negative. Likewise, because the second-best estimate from Redrock is often at the same redshift but of a different class, low values of $\Delta\chi^2$ are not always an indication of degraded confidence in the

redshift estimate. For these reasons, we do not use $\Delta\chi^2$ in the determination of redshifts.

Using the layered automated classification scheme, the target redshift efficiency for the joint tracer and Ly-α forest quasar samples was found to be 65%, a bit lower than found in the visual inspection process. The random redshift error as indicated by pairwise velocity differences was found to be $1 \pm 0.4 \text{ km s}^{-1}$ for the tracer quasars and $1 \pm 0.4 \text{ km s}^{-1}$ for the Ly-α forest quasars. These errors do not include theoretical uncertainties due to internal kinematics, so are therefore a lower bound on the true redshift errors. An updated classification of errors and systematic biases in the DESI quasar redshift estimates can be found in Brodzeller et al. (2023).

## 5.2. Exposure Depth

In determining the performance of redshift classification for all tracers, we generally assumed the effective exposure times from the initial instrument design and pixel-level spectroscopic simulations. For the brighter targets that will be observed in more marginal conditions, these simulations indicated that an effective exposure time of 180 s would be sufficient for robust classification. The individual epochs of BGS and MWS spectra for studies described in this section were therefore tuned to this exposure time, but with significant scatter due to changing conditions. Likewise, simulations indicated that the effective exposure times of 1000 s were sufficient to characterize the fainter LRG, ELG, and quasar targets. Single epochs were tuned to this exposure time for the studies presented above, but again with significant scatter.

The variations in effective exposure times allowed us to assess the redshift efficiency as a function of exposure depth (Figure 14). Here, we present the target redshift efficiency for each of the BGS, LRG, ELG, and quasar samples. As expected, the redshift efficiency values measured above are consistent with the values evaluated at the nominal effective exposure times, with decreasing efficiency at decreasing exposure depth.

The redshift efficiencies presented in Figure 14 allowed us to identify what integration time was best for high-redshift success without overexposing and thus entering the regime of
<figure><img src="image_17.png" /><figcaption>**Figure 13.** The difference in redshift (kilometers per second) between pairs of observations taken of the same ELG target. A linear combination of $log(S/N(F_{\text{O II}}))$ and $log(\Delta\chi^2)$ is used to determine whether a redshift is reliable. The vertical line represents the threshold for the preliminary value where we assume a good redshift estimate. The horizontal line represents the limit at which a redshift discrepancy is considered a catastrophic failure. Left: the distribution of pairs for the ELG\_LOP sample. Right: The distribution for the ELG\_VLO sample. In both panels, a measurement is only included if one spectrum in the pair was characterized as having a redshift estimate in the range $0.6 < z < 1.6$ and if both measurements of the pair have a valid estimate of $S/N(F_{\text{O II}})$ and $\Delta\chi^2$.</figcaption></figure>

conclusive classification or redshift. A large number of quasar spectra with broad emission lines were misclassified as galaxies by Redrock, often at the incorrect redshift. Based on this performance, we developed a method for automated classification based on Redrock estimates of redshift and classification with additional filtering from two customized algorithms. The first of these algorithms provides an estimate of Mg II flux while the second relies on a machine-learning classifier called QuasarNet (Busca & Balland 2018; Farr et al. 2020a).

The first application of these algorithms is designed to recover quasar spectra that were misclassified by Redrock. If a spectrum from the quasar sample is classified by Redrock as a galaxy, we first assess the fits of the Mg II emission line. If a line is detected with an equivalent width between 10 and 200 Å, a significance of at least three standard deviations, and an overall improvement to the fit of $\chi^2 > 16$, then we assume that the redshift estimate was correct and change the classification to that of a quasar. If no significant Mg II flux was detected, we then assess the output of QuasarNet to determine whether the spectrum is actually a quasar at a different redshift. If QuasarNet classifies the object as a quasar with a probability higher than 95%, we compute a new redshift based on the Redrock $\chi^2$ surface evaluated only over a narrow redshift interval ($\Delta z = 0.05$) centered on the QuasarNet redshift estimate.

The second application of these algorithms is designed to recover quasar redshifts that were estimated incorrectly by Redrock. This occurs when both Redrock and QuasarNet identify the object as a quasar but when the two redshifts differ by more than 0.05. Then, as before, we recalculate a new redshift based on the Redrock $\chi^2$ surface evaluated only over a narrow redshift interval ($\Delta z = 0.05$) centered on the QuasarNet redshift estimate.

If either of the conditions described above is satisfied, the spectrum is included in the catalog. In cases where the classification of quasars is not based on the first estimate from Redrock, the value of $\Delta\chi^2$ for the final estimate is negative. Likewise, because the second-best estimate from Redrock is often at the same redshift but of a different class, low values of $\Delta\chi^2$ are not always an indication of degraded confidence in the

redshift estimate. For these reasons, we do not use $\Delta\chi^2$ in the determination of redshifts.

Using the layered automated classification scheme, the target redshift efficiency for the joint tracer and Ly-α forest quasar samples was found to be 65%, a bit lower than found in the visual inspection process. The random redshift error as indicated by pairwise velocity differences was found to be $1 \pm 0.4 \text{ km s}^{-1}$ for the tracer quasars and $1 \pm 0.4 \text{ km s}^{-1}$ for the Ly-α forest quasars. These errors do not include theoretical uncertainties due to internal kinematics, so are therefore a lower bound on the true redshift errors. An updated classification of errors and systematic biases in the DESI quasar redshift estimates can be found in Brodzeller et al. (2023).

## 5.2. Exposure Depth

In determining the performance of redshift classification for all tracers, we generally assumed the effective exposure times from the initial instrument design and pixel-level spectroscopic simulations. For the brighter targets that will be observed in more marginal conditions, these simulations indicated that an effective exposure time of 180 s would be sufficient for robust classification. The individual epochs of BGS and MWS spectra for studies described in this section were therefore tuned to this exposure time, but with significant scatter due to changing conditions. Likewise, simulations indicated that the effective exposure times of 1000 s were sufficient to characterize the fainter LRG, ELG, and quasar targets. Single epochs were tuned to this exposure time for the studies presented above, but again with significant scatter.

The variations in effective exposure times allowed us to assess the redshift efficiency as a function of exposure depth (Figure 14). Here, we present the target redshift efficiency for each of the BGS, LRG, ELG, and quasar samples. As expected, the redshift efficiency values measured above are consistent with the values evaluated at the nominal effective exposure times, with decreasing efficiency at decreasing exposure depth.

The redshift efficiencies presented in Figure 14 allowed us to identify what integration time was best for high-redshift success without overexposing and thus entering the regime of
<figure><img src="image_17.png" /><figcaption>**Figure 14.** Target redshift efficiency and 68% confidence intervals normalized to the efficiency at the fiducial exposure times (vertical dashed lines) for each of the BGS Bright, LRG, ELG_LOP, and quasar samples. BGS Faint and ELG_VLO targets are not included because they overlap in redshift range with higher priority targets of a similar class. Effective exposure time determined for each epoch is computed as described in Section 3.3.</figcaption></figure>

diminishing returns. The ELG sample set the pace for integrations, where we see a 3% decrease in target redshift efficiency in the ELG_LOP sample when effective exposure times are decreased from 800 to 700 s. However, for the ELG samples, the slope of the efficiency curve flattens at effective exposure times larger than 800 s, indicating an approach to diminishing returns. The target efficiency in the ELG_LOP sample only increases from 67.8% to 68.8% as effective exposure times are increased from 800 to 1200 s. The change in the LRG redshift efficiencies is even lower over this range, while the quasar redshift efficiency climbs from 91.1% to 94.2%. Likewise, the change in BGS Bright target redshift efficiency only changes by 2% as effective exposure times are increased from 120 to 210 s.

These results were determined from the target selection validation program, and we find consistent behavior in the One-Percent Survey. As a balance between consistent redshift efficiency and areal coverage, we therefore plan effective exposure times of 1000 s for the LRG, ELG, and QSO programs and 180 s for the BGS and MWS programs. This stability in redshift efficiency demonstrates that the clustering analyses will be subject to peak-to-peak variations in redshift efficiency of less than 3.4% as long as estimates with the real-time ETC are accurate to 20%. As described in Section 3.3, the expected scatter in real-time exposure time estimates is expected to be less than 10%.

While effective exposure times are expected to be the primary driver for redshift efficiency, it is equally important to assess whether survey speed (Section 3.3) plays a role. The nominal survey plan prescribes observations to LRG, ELG, and quasar targets when the survey speeds exceed 0.4 and observations to BGS and MWS targets when the survey speed is within a range of $[1/6, 0.4]$. During times of slower survey speeds due to degraded observing conditions, observing will be dedicated to a backup program of bright stellar targets. That backup program is described elsewhere (A. Cooper et al. 2023, in preparation).

It is possible that the lower survey speeds will lead to reduced redshift efficiencies for BGS, LRG, ELG, or quasar targets even at a constant effective exposure time. For example,

exposures taken at lower survey speeds may be more susceptible to sky subtraction or other residuals in the limit of lower signal-to-noise. However, studies revealed very little change in the redshift efficiency for BGS, LRG, ELG, or quasar targets with survey speeds that were below the nominal thresholds. As with the dependence on effective exposure times, the relationship between survey speed and redshift efficiency observed in the One-Percent Survey is consistent with what was found in target selection validation, thus confirming the scheme for allocating spectroscopic time between higher- and lower-redshift samples.

### 5.3. Overall Performance

With effective exposure times of 1000 and 180 s for dark time and bright time, respectively, survey simulations indicate that DESI will complete a 14,900 deg² footprint in 5 yr. From the central 14,000 deg² of that footprint, the target selection algorithms and fiber assignment efficiencies presented in Section 4, and redshift performance reported in this section, we estimate the final statistics for the 5 yr survey. The redshift distributions for spectroscopically confirmed, extragalactic targets are shown in Figure 15. In total, we expect a final spectroscopic sample of 7.2 million unique stars (over all Bright tiles, including faint sources), 36.12 million unique galaxies, and 2.87 million unique quasars with reliable redshift estimates. In Table 5 and Table 6, those results are compared to the science requirements crafted in 2014 that were used to inform the DESI instrument design (DESI Collaboration et al. 2022). Below, we highlight some expected changes to the survey arising from the SV results.

Across the LRG, ELG, and quasar target samples, we expect to exceed the design requirements by a significant margin for random redshift errors. We also expect to exceed the design requirements for catastrophic redshift failure rates for the galaxy samples by a large margin, while also surpassing the design requirement for quasars if the definition of a catastrophic failure is relaxed from 1000 to 3000 km s⁻¹. Further improvements to the data reductions and redshift classification schemes may lead to better performance yet.

The SV results led the DESI collaboration to reallocate the fibers relative to the initial design to significantly increase the LRG and quasar sample sizes while keeping their combined observational cost almost unchanged. It was originally assumed that LRG targets fainter than a z-band magnitude of 20 would require effective exposure times longer than 1000 s, leading to an average of 2000 s per target (two exposures) to achieve an adequate number of reliable redshift estimates. Based on the high-redshift success rates found in SV, the observational program was updated to only assign a single epoch of observation to all LRG targets, even those with magnitudes as faint as $z=20.6$. With this modification, the target density was increased from 350 to 624 deg⁻². The observational cost is 25 exposures deg⁻² lower than the original expectation, but now with 80% more targets expected to be given a reliable redshift estimate. The results from SV revealed that quasars could still be identified at a high confidence beyond the boundaries of the original selection. By increasing the target density by 20% to 311 deg⁻², we expect a 20% increase in the number of Ly-α quasars and nearly the same fractional increase in the number of $z<2.1$ quasars. With an average of 3.4 exposures for each high-redshift quasar, the total cost of this
<figure><img src="image_18.png" /><figcaption>**Figure 14.** Target redshift efficiency and 68% confidence intervals normalized to the efficiency at the fiducial exposure times (vertical dashed lines) for each of the BGS Bright, LRG, ELG_LOP, and quasar samples. BGS Faint and ELG_VLO targets are not included because they overlap in redshift range with higher priority targets of a similar class. Effective exposure time determined for each epoch is computed as described in Section 3.3.</figcaption></figure>

diminishing returns. The ELG sample set the pace for integrations, where we see a 3% decrease in target redshift efficiency in the ELG_LOP sample when effective exposure times are decreased from 800 to 700 s. However, for the ELG samples, the slope of the efficiency curve flattens at effective exposure times larger than 800 s, indicating an approach to diminishing returns. The target efficiency in the ELG_LOP sample only increases from 67.8% to 68.8% as effective exposure times are increased from 800 to 1200 s. The change in the LRG redshift efficiencies is even lower over this range, while the quasar redshift efficiency climbs from 91.1% to 94.2%. Likewise, the change in BGS Bright target redshift efficiency only changes by 2% as effective exposure times are increased from 120 to 210 s.

These results were determined from the target selection validation program, and we find consistent behavior in the One-Percent Survey. As a balance between consistent redshift efficiency and areal coverage, we therefore plan effective exposure times of 1000 s for the LRG, ELG, and QSO programs and 180 s for the BGS and MWS programs. This stability in redshift efficiency demonstrates that the clustering analyses will be subject to peak-to-peak variations in redshift efficiency of less than 3.4% as long as estimates with the real-time ETC are accurate to 20%. As described in Section 3.3, the expected scatter in real-time exposure time estimates is expected to be less than 10%.

While effective exposure times are expected to be the primary driver for redshift efficiency, it is equally important to assess whether survey speed (Section 3.3) plays a role. The nominal survey plan prescribes observations to LRG, ELG, and quasar targets when the survey speeds exceed 0.4 and observations to BGS and MWS targets when the survey speed is within a range of $[\frac{1}{6}, 0.4]$. During times of slower survey speeds due to degraded observing conditions, observing will be dedicated to a backup program of bright stellar targets. That backup program is described elsewhere (A. Cooper et al. 2023, in preparation).

It is possible that the lower survey speeds will lead to reduced redshift efficiencies for BGS, LRG, ELG, or quasar targets even at a constant effective exposure time. For example,

exposures taken at lower survey speeds may be more susceptible to sky subtraction or other residuals in the limit of lower signal-to-noise. However, studies revealed very little change in the redshift efficiency for BGS, LRG, ELG, or quasar targets with survey speeds that were below the nominal thresholds. As with the dependence on effective exposure times, the relationship between survey speed and redshift efficiency observed in the One-Percent Survey is consistent with what was found in target selection validation, thus confirming the scheme for allocating spectroscopic time between higher- and lower-redshift samples.

### 5.3. Overall Performance

With effective exposure times of 1000 and 180 s for dark time and bright time, respectively, survey simulations indicate that DESI will complete a 14,900 deg² footprint in 5 yr. From the central 14,000 deg² of that footprint, the target selection algorithms and fiber assignment efficiencies presented in Section 4, and redshift performance reported in this section, we estimate the final statistics for the 5 yr survey. The redshift distributions for spectroscopically confirmed, extragalactic targets are shown in Figure 15. In total, we expect a final spectroscopic sample of 7.2 million unique stars (over all Bright tiles, including faint sources), 36.12 million unique galaxies, and 2.87 million unique quasars with reliable redshift estimates. In Table 5 and Table 6, those results are compared to the science requirements crafted in 2014 that were used to inform the DESI instrument design (DESI Collaboration et al. 2022). Below, we highlight some expected changes to the survey arising from the SV results.

Across the LRG, ELG, and quasar target samples, we expect to exceed the design requirements by a significant margin for random redshift errors. We also expect to exceed the design requirements for catastrophic redshift failure rates for the galaxy samples by a large margin, while also surpassing the design requirement for quasars if the definition of a catastrophic failure is relaxed from 1000 to 3000 km s⁻¹. Further improvements to the data reductions and redshift classification schemes may lead to better performance yet.

The SV results led the DESI collaboration to reallocate the fibers relative to the initial design to significantly increase the LRG and quasar sample sizes while keeping their combined observational cost almost unchanged. It was originally assumed that LRG targets fainter than a z-band magnitude of 20 would require effective exposure times longer than 1000 s, leading to an average of 2000 s per target (two exposures) to achieve an adequate number of reliable redshift estimates. Based on the high-redshift success rates found in SV, the observational program was updated to only assign a single epoch of observation to all LRG targets, even those with magnitudes as faint as z = 20.6. With this modification, the target density was increased from 350 to 624 deg⁻². The observational cost is 25 exposures deg⁻² lower than the original expectation, but now with 80% more targets expected to be given a reliable redshift estimate. The results from SV revealed that quasars could still be identified at a high confidence beyond the boundaries of the original selection. By increasing the target density by 20% to 311 deg⁻², we expect a 20% increase in the number of Ly-α quasars and nearly the same fractional increase in the number of z < 2.1 quasars. With an average of 3.4 exposures for each high-redshift quasar, the total cost of this
<figure><img src="image_18.png" /><figcaption>**Figure 15.** The surface density as a function of redshift for each extragalactic tracer in the DESI spectroscopic sample. Only objects with a successful fiber assignment and reliable redshift are shown, and no corrections are made for incompleteness or interlopers due to catastrophic failures in redshift assignment. Left: Redshift distribution for galaxies that will be observed in bright conditions. The black curve corresponds to the projections from a single magnitude-limited BGS sample as assumed in the original design (DESI Collaboration et al. 2016a). Right: Redshift distribution for galaxies and quasars that will be observed in dark conditions. The black curve (design) corresponds to the predictions from an LRG sample over 0.6 < z < 0.8, an ELG sample over 0.8 < z < 1.6, and a quasar sample at higher redshifts as assumed in the original design (final design review; DESI Collaboration et al. 2016a).</figcaption></figure>

program is 450 exposures deg$^{-2}$, only 30 more than the original design.

While the LRG and quasar programs are expected to produce significantly larger clustering samples at effectively the same observational cost, the ELG program falls somewhat below what was originally planned in both target density and size of the clustering sample. First, the assumed fiber assignment efficiencies of 80% turned out to be slightly optimistic, as 69% of the ELG_LOP sample is actually assigned a fiber. Second, it proved challenging to identify the highest-redshift galaxies from grz imaging data beyond a certain density, so we reduced the target density of the prime sample from 2400 to 1941 deg$^{-2}$. We provided the remaining targets from the lower priority ELG_VLO selection. This split in the sample helped to preserve a higher fiber assignment efficiency for the targets most likely to produce a reliable redshift in the range not overlapping with the LRG sample. A spectroscopic sample size of 400 deg$^{-2}$ was originally assumed over $1.1 < z < 1.6$ (DESI Collaboration et al. 2016a), but as shown in Figure 15, the ELG_LOP will exceed this expectation with a surface density of 450 deg$^{-2}$. Even though the target density and total clustering sample sizes are lower than expected, the final selection produces a more efficient program in the redshift range that is most distinct from the other clustering samples.

Finally, even though the BGS and MWS samples did not drive the requirements for instrument design, the final samples still exceed expectations. A BGS target sample of 700 deg$^{-2}$ was presented in the final survey design (DESI Collaboration et al. 2016a), whereas 854 deg$^{-2}$ can be identified from a magnitude-limited sample and classified at high efficiency. Likewise, the BGS Faint and MWS samples were not presented in detail, but, combined, are expected to produce more than 10 million unique spectra over 5 yr.

We repeated the study of total redshift efficiency and target redshift efficiency on the One-Percent Survey data. The performance of the spectroscopic classification confirmed the redshift efficiencies reported here, thus validating the expected tracer counts for cosmology forecasts. More detailed studies for each tracer such as differential efficiency rates as a function of

magnitude can be found in the dedicated target selection and visual inspection papers.

# 6. Cosmological Forecasts

Based on the derived target selection densities, fiber assignment efficiencies, and redshift efficiencies, we forecast the cosmological constraints for the 14,000 deg$^2$ DESI program. We first demonstrate the statistical precision that we are expecting on the measurements of the distance scale through BAO and the growth of structure through RSD. From these forecasts, we predict the precision expected on the cosmological parameters in various combinations of DESI BAO and RSD measurements both alone and with external data sets.

## 6.1. BAO and RSD Forecasts

The number density and redshift distribution over the 14,000 deg$^2$ footprint for each tracer used in the forecasts is shown in Table 7. These predicted number densities, along with an assumption on bias as described in the next paragraph, allow us to predict the sensitivity to $D_A(z)/r_d$, $H(z)r_d$, and $f\sigma_8$ in each redshift interval. Here, $D_A$ is the angular diameter distance, $H$ is the Hubble parameter, $r_d$ is the sound horizon at the drag epoch, $f$ is the growth factor, and $\sigma_8$ is the amplitude of mass fluctuations in spheres of $8 h^{-1}$ Mpc; note that the quantity $f\sigma_8$ is essentially the amplitude of the velocity power spectrum and is readily probed by RSD measurements. An additional parameter $R$ is often used to represent the precision resulting from the optimal combination of $D_A/r_d$ and $Hr_d$ measurements. In redshift bins with multiple tracers, we use the densest tracer to keep our forecasts conservative. The left panel of Figure 16 shows the fractional uncertainty on the volume-averaged BAO measurement relative to the cosmic-variance limit for a 14,000 deg$^2$ survey. The right panel shows the fractional uncertainty on the growth of structure measurements from RSD.

For $z < 0.4$, we forecast constraints using the BGS sample assuming that bias evolves as $b_{\text{BGS}}(z) = 1.34/D(z)$, where $D(z)$ is the linear growth factor normalized by $D(z=0) = 1$. Over the redshift range $0.4 < z < 1.1$, we use the LRG sample assuming $b_{\text{LRG}}(z) = 1.7/D(z)$. For the ELG sample, we use
<figure><img src="image_19.png" /><figcaption>**Figure 15.** The surface density as a function of redshift for each extragalactic tracer in the DESI spectroscopic sample. Only objects with a successful fiber assignment and reliable redshift are shown, and no corrections are made for incompleteness or interlopers due to catastrophic failures in redshift assignment. Left: Redshift distribution for galaxies that will be observed in bright conditions. The black curve corresponds to the projections from a single magnitude-limited BGS sample as assumed in the original design (DESI Collaboration et al. 2016a). Right: Redshift distribution for galaxies and quasars that will be observed in dark conditions. The black curve (design) corresponds to the predictions from an LRG sample over 0.6 < z < 0.8, an ELG sample over 0.8 < z < 1.6, and a quasar sample at higher redshifts as assumed in the original design (final design review; DESI Collaboration et al. 2016a).</figcaption></figure>

program is 450 exposures deg$^{-2}$, only 30 more than the original design.

While the LRG and quasar programs are expected to produce significantly larger clustering samples at effectively the same observational cost, the ELG program falls somewhat below what was originally planned in both target density and size of the clustering sample. First, the assumed fiber assignment efficiencies of 80% turned out to be slightly optimistic, as 69% of the ELG_LOP sample is actually assigned a fiber. Second, it proved challenging to identify the highest-redshift galaxies from grz imaging data beyond a certain density, so we reduced the target density of the prime sample from 2400 to 1941 deg$^{-2}$. We provided the remaining targets from the lower priority ELG_VLO selection. This split in the sample helped to preserve a higher fiber assignment efficiency for the targets most likely to produce a reliable redshift in the range not overlapping with the LRG sample. A spectroscopic sample size of 400 deg$^{-2}$ was originally assumed over 1.1 < z < 1.6 (DESI Collaboration et al. 2016a), but as shown in Figure 15, the ELG_LOP will exceed this expectation with a surface density of 450 deg$^{-2}$. Even though the target density and total clustering sample sizes are lower than expected, the final selection produces a more efficient program in the redshift range that is most distinct from the other clustering samples.

Finally, even though the BGS and MWS samples did not drive the requirements for instrument design, the final samples still exceed expectations. A BGS target sample of 700 deg$^{-2}$ was presented in the final survey design (DESI Collaboration et al. 2016a), whereas 854 deg$^{-2}$ can be identified from a magnitude-limited sample and classified at high efficiency. Likewise, the BGS Faint and MWS samples were not presented in detail, but, combined, are expected to produce more than 10 million unique spectra over 5 yr.

We repeated the study of total redshift efficiency and target redshift efficiency on the One-Percent Survey data. The performance of the spectroscopic classification confirmed the redshift efficiencies reported here, thus validating the expected tracer counts for cosmology forecasts. More detailed studies for each tracer such as differential efficiency rates as a function of

magnitude can be found in the dedicated target selection and visual inspection papers.

# 6. Cosmological Forecasts

Based on the derived target selection densities, fiber assignment efficiencies, and redshift efficiencies, we forecast the cosmological constraints for the 14,000 deg$^2$ DESI program. We first demonstrate the statistical precision that we are expecting on the measurements of the distance scale through BAO and the growth of structure through RSD. From these forecasts, we predict the precision expected on the cosmological parameters in various combinations of DESI BAO and RSD measurements both alone and with external data sets.

## 6.1. BAO and RSD Forecasts

The number density and redshift distribution over the 14,000 deg$^2$ footprint for each tracer used in the forecasts is shown in Table 7. These predicted number densities, along with an assumption on bias as described in the next paragraph, allow us to predict the sensitivity to $D_A(z)/r_d$, $H(z)r_d$, and $f\sigma_8$ in each redshift interval. Here, $D_A$ is the angular diameter distance, $H$ is the Hubble parameter, $r_d$ is the sound horizon at the drag epoch, $f$ is the growth factor, and $\sigma_8$ is the amplitude of mass fluctuations in spheres of 8 $h^{-1}$ Mpc; note that the quantity $f\sigma_8$ is essentially the amplitude of the velocity power spectrum and is readily probed by RSD measurements. An additional parameter $R$ is often used to represent the precision resulting from the optimal combination of $D_A/r_d$ and $Hr_d$ measurements. In redshift bins with multiple tracers, we use the densest tracer to keep our forecasts conservative. The left panel of Figure 16 shows the fractional uncertainty on the volume-averaged BAO measurement relative to the cosmic-variance limit for a 14,000 deg$^2$ survey. The right panel shows the fractional uncertainty on the growth of structure measurements from RSD.

For $z < 0.4$, we forecast constraints using the BGS sample assuming that bias evolves as $b_{\text{BGS}}(z) = 1.34/D(z)$, where $D(z)$ is the linear growth factor normalized by $D(z=0) = 1$. Over the redshift range $0.4 < z < 1.1$, we use the LRG sample assuming $b_{\text{LRG}}(z) = 1.7/D(z)$. For the ELG sample, we use
<table><caption>**Table 7**
Cosmological Tracers and Forecasts of Precision (×100%) on BAO and RSD Measurements</caption><thead><tr><th>Redshift</th><th>Surface Density<br>(deg<sup>-2</sup>)</th><th>nP<sub>k=0.14,μ=0.6</sub></th><th>V<sub>eff</sub><br>(h<sup>-3</sup> Gpc<sup>3</sup>)</th><th>σD<sub>h</sub>/d<br>D<sub>A</sub>/r<sub>d</sub><br>(%)</th><th>σH<sub>0</sub><br>H<sub>0</sub><br>(%)</th><th>σR<sup>a</sup><br>R<br>(%)</th><th>σf<sub>8</sub><br>f<sub>8</sub><br>(%)</th></tr></thead><tbody><tr><td colspan="8" style="text-align: center; font-weight: bold;">BGS BRIGHT</td></tr><tr><td>0.0 &lt; z &lt; 0.1</td><td>101.1</td><td>338.54</td><td>0.04</td><td>6.65</td><td>13.92</td><td>4.95</td><td>31.64</td></tr><tr><td>0.1 &lt; z &lt; 0.2</td><td>231.3</td><td>122.16</td><td>0.22</td><td>2.57</td><td>5.40</td><td>1.91</td><td>12.04</td></tr><tr><td>0.2 &lt; z &lt; 0.3</td><td>216.9</td><td>47.11</td><td>0.54</td><td>1.64</td><td>3.41</td><td>1.21</td><td>7.54</td></tr><tr><td>0.3 &lt; z &lt; 0.4</td><td>97.3</td><td>12.15</td><td>0.83</td><td>1.37</td><td>2.70</td><td>0.99</td><td>5.76</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">LRG</td></tr><tr><td>0.4 &lt; z &lt; 0.5</td><td>47.5</td><td>6.12</td><td>1.06</td><td>1.25</td><td>2.38</td><td>0.88</td><td>5.96</td></tr><tr><td>0.5 &lt; z &lt; 0.6</td><td>65.6</td><td>6.35</td><td>1.42</td><td>1.05</td><td>1.99</td><td>0.74</td><td>5.16</td></tr><tr><td>0.6 &lt; z &lt; 0.7</td><td>80.0</td><td>6.21</td><td>1.76</td><td>0.92</td><td>1.74</td><td>0.65</td><td>4.67</td></tr><tr><td>0.7 &lt; z &lt; 0.8</td><td>93.2</td><td>6.08</td><td>2.07</td><td>0.84</td><td>1.56</td><td>0.59</td><td>4.34</td></tr><tr><td>0.8 &lt; z &lt; 0.9</td><td>99.3</td><td>5.64</td><td>2.32</td><td>0.78</td><td>1.44</td><td>0.55</td><td>4.14</td></tr><tr><td>0.9 &lt; z &lt; 1.0</td><td>63.7</td><td>3.23</td><td>2.09</td><td>0.87</td><td>1.52</td><td>0.59</td><td>4.19</td></tr><tr><td>1.0 &lt; z &lt; 1.1</td><td>28.3</td><td>1.31</td><td>1.25</td><td>1.25</td><td>2.04</td><td>0.83</td><td>4.77</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">ELG_LOP</td></tr><tr><td>1.1 &lt; z &lt; 1.2</td><td>108.0</td><td>1.37</td><td>1.40</td><td>1.24</td><td>1.80</td><td>0.79</td><td>2.58</td></tr><tr><td>1.2 &lt; z &lt; 1.3</td><td>103.6</td><td>1.23</td><td>1.35</td><td>1.26</td><td>1.80</td><td>0.80</td><td>2.62</td></tr><tr><td>1.3 &lt; z &lt; 1.4</td><td>97.1</td><td>1.09</td><td>1.26</td><td>1.30</td><td>1.82</td><td>0.82</td><td>2.69</td></tr><tr><td>1.4 &lt; z &lt; 1.5</td><td>87.7</td><td>0.93</td><td>1.13</td><td>1.37</td><td>1.89</td><td>0.87</td><td>2.80</td></tr><tr><td>1.5 &lt; z &lt; 1.6</td><td>55.4</td><td>0.57</td><td>0.65</td><td>1.87</td><td>2.46</td><td>1.17</td><td>3.34</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">Quasars</td></tr><tr><td>1.6 &lt; z &lt; 1.7</td><td>12.1</td><td>0.22</td><td>0.17</td><td>3.39</td><td>4.76</td><td>2.16</td><td>7.30</td></tr><tr><td>1.7 &lt; z &lt; 1.8</td><td>11.8</td><td>0.21</td><td>0.16</td><td>3.48</td><td>4.87</td><td>2.21</td><td>7.63</td></tr><tr><td>1.8 &lt; z &lt; 1.9</td><td>11.1</td><td>0.19</td><td>0.14</td><td>3.67</td><td>5.14</td><td>2.34</td><td>8.17</td></tr><tr><td>1.9 &lt; z &lt; 2.0</td><td>10.6</td><td>0.18</td><td>0.13</td><td>3.83</td><td>5.36</td><td>2.44</td><td>8.66</td></tr><tr><td>2.0 &lt; z &lt; 2.1</td><td>9.5</td><td>0.16</td><td>0.10</td><td>4.22</td><td>5.90</td><td>2.69</td><td>9.58</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">Ly-α autocorrelation and quasar—Ly-α cross-correlation<sup>b</sup></td></tr><tr><td>2.1 &lt; z &lt; 2.2</td><td>8.8</td><td></td><td></td><td>2.02</td><td>2.16</td><td>1.1</td><td></td></tr><tr><td>2.2 &lt; z &lt; 2.3</td><td>8.0</td><td></td><td></td><td>2.14</td><td>2.24</td><td>1.15</td><td></td></tr><tr><td>2.3 &lt; z &lt; 2.4</td><td>7.2</td><td></td><td></td><td>2.33</td><td>2.36</td><td>1.22</td><td></td></tr><tr><td>2.4 &lt; z &lt; 2.5</td><td>6.2</td><td></td><td></td><td>2.56</td><td>2.52</td><td>1.32</td><td></td></tr><tr><td>2.5 &lt; z &lt; 2.6</td><td>5.3</td><td></td><td></td><td>2.9</td><td>2.77</td><td>1.47</td><td></td></tr><tr><td>2.6 &lt; z &lt; 2.7</td><td>4.4</td><td></td><td></td><td>3.38</td><td>3.11</td><td>1.67</td><td></td></tr><tr><td>2.7 &lt; z &lt; 2.8</td><td>3.6</td><td></td><td></td><td>3.95</td><td>3.5</td><td>1.91</td><td></td></tr><tr><td>2.8 &lt; z &lt; 2.9</td><td>3.3</td><td></td><td></td><td>4.69</td><td>4.05</td><td>2.23</td><td></td></tr><tr><td>2.9 &lt; z &lt; 3.0</td><td>2.6</td><td></td><td></td><td>5.59</td><td>4.71</td><td>2.62</td><td></td></tr><tr><td>3.0 &lt; z &lt; 3.1</td><td>2.2</td><td></td><td></td><td>6.73</td><td>5.51</td><td>3.09</td><td></td></tr><tr><td>3.1 &lt; z &lt; 3.2</td><td>1.7</td><td></td><td></td><td>8.47</td><td>6.78</td><td>3.84</td><td></td></tr><tr><td>3.2 &lt; z &lt; 3.3</td><td>1.4</td><td></td><td></td><td>10.73</td><td>8.41</td><td>4.8</td><td></td></tr><tr><td>3.3 &lt; z &lt; 3.4</td><td>1.1</td><td></td><td></td><td>14.48</td><td>11.1</td><td>6.4</td><td></td></tr><tr><td>3.4 &lt; z &lt; 3.5</td><td>0.7</td><td></td><td></td><td>19.92</td><td>14.8</td><td>8.62</td><td></td></tr></tbody></table>

**Notes.** Estimates of covariance between BAO and RSD parameters can be found with other supplemental data, as described immediately following the conclusion.

<sup>a</sup> The value *R* represents the precision resulting from the optimal combination of *D*<sub>A</sub>(*z*)/*r*<sub>d</sub> and *H*(*z*)*r*<sub>d</sub> measurements. In most cases, it can be considered a volume-averaged constraint on the BAO distance scale.

<sup>b</sup> Ly-α quasars will be used for both autocorrelation and cross-correlation measurements. Because the Ly-α forest is a continuous tracer, we do not compute volume density or effective volume.

$b_{\text{ELG}}(z) = 0.84/D(z)$ based on Mostek et al. (2013), over the redshift range $1.1 < z < 1.6$. We use quasars in two different ways. We consider them as discrete tracers of the matter density field to forecast constraints over the range $1.6 < z < 2.1$ assuming a bias of $b_{\text{QSO}}(z) = 1.2/D(z)$, loosely based on Ross et al. (2009). We also consider the line-of-sight absorption information to quasars in order to extract the clustering of the matter density field through the Ly-α forest. We assume $b_{\text{QSO}}(z) = 1.1/D(z)$ for redshifts $2.1 < z < 3.5$ when using

quasars for measurements of the autocorrelation of the Ly-α forest and for the cross-correlation between the Ly-α forest and quasars (e.g., Font-Ribera et al. 2014b).

For the $z > 2.1$ BAO projections involving the Ly-α forest, we use the algorithm and code described in Font-Ribera et al. (2014a). For the rest of our forecasts, we use the software GoFish,<sup>114</sup> a Fisher forecast tool for DESI galaxy clustering

<footnote n="114"><sup>114</sup> https://github.com/ladosamushia/GoFish</footnote>
<table><caption>**Table 7**
Cosmological Tracers and Forecasts of Precision (×100%) on BAO and RSD Measurements</caption><thead><tr><th>Redshift</th><th>Surface Density<br>(deg<sup>-2</sup>)</th><th>nP<sub>k=0.14,μ=0.6</sub></th><th>V<sub>eff</sub><br>(h<sup>-3</sup> Gpc<sup>3</sup>)</th><th>σD<sub>h</sub>/d<br>D<sub>A</sub>/r<sub>d</sub><br>(%)</th><th>σH<sub>0</sub><br>H<sub>0</sub><br>(%)</th><th>σR<sup>a</sup><br>R<br>(%)</th><th>σf<sub>8</sub><br>f<sub>8</sub><br>(%)</th></tr></thead><tbody><tr><td colspan="8" style="text-align: center; font-weight: bold;">BGS BRIGHT</td></tr><tr><td>0.0 &lt; z &lt; 0.1</td><td>101.1</td><td>338.54</td><td>0.04</td><td>6.65</td><td>13.92</td><td>4.95</td><td>31.64</td></tr><tr><td>0.1 &lt; z &lt; 0.2</td><td>231.3</td><td>122.16</td><td>0.22</td><td>2.57</td><td>5.40</td><td>1.91</td><td>12.04</td></tr><tr><td>0.2 &lt; z &lt; 0.3</td><td>216.9</td><td>47.11</td><td>0.54</td><td>1.64</td><td>3.41</td><td>1.21</td><td>7.54</td></tr><tr><td>0.3 &lt; z &lt; 0.4</td><td>97.3</td><td>12.15</td><td>0.83</td><td>1.37</td><td>2.70</td><td>0.99</td><td>5.76</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">LRG</td></tr><tr><td>0.4 &lt; z &lt; 0.5</td><td>47.5</td><td>6.12</td><td>1.06</td><td>1.25</td><td>2.38</td><td>0.88</td><td>5.96</td></tr><tr><td>0.5 &lt; z &lt; 0.6</td><td>65.6</td><td>6.35</td><td>1.42</td><td>1.05</td><td>1.99</td><td>0.74</td><td>5.16</td></tr><tr><td>0.6 &lt; z &lt; 0.7</td><td>80.0</td><td>6.21</td><td>1.76</td><td>0.92</td><td>1.74</td><td>0.65</td><td>4.67</td></tr><tr><td>0.7 &lt; z &lt; 0.8</td><td>93.2</td><td>6.08</td><td>2.07</td><td>0.84</td><td>1.56</td><td>0.59</td><td>4.34</td></tr><tr><td>0.8 &lt; z &lt; 0.9</td><td>99.3</td><td>5.64</td><td>2.32</td><td>0.78</td><td>1.44</td><td>0.55</td><td>4.14</td></tr><tr><td>0.9 &lt; z &lt; 1.0</td><td>63.7</td><td>3.23</td><td>2.09</td><td>0.87</td><td>1.52</td><td>0.59</td><td>4.19</td></tr><tr><td>1.0 &lt; z &lt; 1.1</td><td>28.3</td><td>1.31</td><td>1.25</td><td>1.25</td><td>2.04</td><td>0.83</td><td>4.77</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">ELG_LOP</td></tr><tr><td>1.1 &lt; z &lt; 1.2</td><td>108.0</td><td>1.37</td><td>1.40</td><td>1.24</td><td>1.80</td><td>0.79</td><td>2.58</td></tr><tr><td>1.2 &lt; z &lt; 1.3</td><td>103.6</td><td>1.23</td><td>1.35</td><td>1.26</td><td>1.80</td><td>0.80</td><td>2.62</td></tr><tr><td>1.3 &lt; z &lt; 1.4</td><td>97.1</td><td>1.09</td><td>1.26</td><td>1.30</td><td>1.82</td><td>0.82</td><td>2.69</td></tr><tr><td>1.4 &lt; z &lt; 1.5</td><td>87.7</td><td>0.93</td><td>1.13</td><td>1.37</td><td>1.89</td><td>0.87</td><td>2.80</td></tr><tr><td>1.5 &lt; z &lt; 1.6</td><td>55.4</td><td>0.57</td><td>0.65</td><td>1.87</td><td>2.46</td><td>1.17</td><td>3.34</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">Quasars</td></tr><tr><td>1.6 &lt; z &lt; 1.7</td><td>12.1</td><td>0.22</td><td>0.17</td><td>3.39</td><td>4.76</td><td>2.16</td><td>7.30</td></tr><tr><td>1.7 &lt; z &lt; 1.8</td><td>11.8</td><td>0.21</td><td>0.16</td><td>3.48</td><td>4.87</td><td>2.21</td><td>7.63</td></tr><tr><td>1.8 &lt; z &lt; 1.9</td><td>11.1</td><td>0.19</td><td>0.14</td><td>3.67</td><td>5.14</td><td>2.34</td><td>8.17</td></tr><tr><td>1.9 &lt; z &lt; 2.0</td><td>10.6</td><td>0.18</td><td>0.13</td><td>3.83</td><td>5.36</td><td>2.44</td><td>8.66</td></tr><tr><td>2.0 &lt; z &lt; 2.1</td><td>9.5</td><td>0.16</td><td>0.10</td><td>4.22</td><td>5.90</td><td>2.69</td><td>9.58</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">Ly-α autocorrelation and quasar—Ly-α cross-correlation<sup>b</sup></td></tr><tr><td>2.1 &lt; z &lt; 2.2</td><td>8.8</td><td></td><td></td><td>2.02</td><td>2.16</td><td>1.1</td><td></td></tr><tr><td>2.2 &lt; z &lt; 2.3</td><td>8.0</td><td></td><td></td><td>2.14</td><td>2.24</td><td>1.15</td><td></td></tr><tr><td>2.3 &lt; z &lt; 2.4</td><td>7.2</td><td></td><td></td><td>2.33</td><td>2.36</td><td>1.22</td><td></td></tr><tr><td>2.4 &lt; z &lt; 2.5</td><td>6.2</td><td></td><td></td><td>2.56</td><td>2.52</td><td>1.32</td><td></td></tr><tr><td>2.5 &lt; z &lt; 2.6</td><td>5.3</td><td></td><td></td><td>2.9</td><td>2.77</td><td>1.47</td><td></td></tr><tr><td>2.6 &lt; z &lt; 2.7</td><td>4.4</td><td></td><td></td><td>3.38</td><td>3.11</td><td>1.67</td><td></td></tr><tr><td>2.7 &lt; z &lt; 2.8</td><td>3.6</td><td></td><td></td><td>3.95</td><td>3.5</td><td>1.91</td><td></td></tr><tr><td>2.8 &lt; z &lt; 2.9</td><td>3.3</td><td></td><td></td><td>4.69</td><td>4.05</td><td>2.23</td><td></td></tr><tr><td>2.9 &lt; z &lt; 3.0</td><td>2.6</td><td></td><td></td><td>5.59</td><td>4.71</td><td>2.62</td><td></td></tr><tr><td>3.0 &lt; z &lt; 3.1</td><td>2.2</td><td></td><td></td><td>6.73</td><td>5.51</td><td>3.09</td><td></td></tr><tr><td>3.1 &lt; z &lt; 3.2</td><td>1.7</td><td></td><td></td><td>8.47</td><td>6.78</td><td>3.84</td><td></td></tr><tr><td>3.2 &lt; z &lt; 3.3</td><td>1.4</td><td></td><td></td><td>10.73</td><td>8.41</td><td>4.8</td><td></td></tr><tr><td>3.3 &lt; z &lt; 3.4</td><td>1.1</td><td></td><td></td><td>14.48</td><td>11.1</td><td>6.4</td><td></td></tr><tr><td>3.4 &lt; z &lt; 3.5</td><td>0.7</td><td></td><td></td><td>19.92</td><td>14.8</td><td>8.62</td><td></td></tr></tbody></table>

**Notes.** Estimates of covariance between BAO and RSD parameters can be found with other supplemental data, as described immediately following the conclusion.

<sup>a</sup> The value *R* represents the precision resulting from the optimal combination of *D*<sub>A</sub>(*z*)/*r*<sub>d</sub> and *H*(*z*)*r*<sub>d</sub> measurements. In most cases, it can be considered a volume-averaged constraint on the BAO distance scale.

<sup>b</sup> Ly-α quasars will be used for both autocorrelation and cross-correlation measurements. Because the Ly-α forest is a continuous tracer, we do not compute volume density or effective volume.

$b_{\text{ELG}}(z) = 0.84/D(z)$ based on Mostek et al. (2013), over the redshift range $1.1 < z < 1.6$. We use quasars in two different ways. We consider them as discrete tracers of the matter density field to forecast constraints over the range $1.6 < z < 2.1$ assuming a bias of $b_{\text{QSO}}(z) = 1.2/D(z)$, loosely based on Ross et al. (2009). We also consider the line-of-sight absorption information to quasars in order to extract the clustering of the matter density field through the Ly-α forest. We assume $b_{\text{QSO}}(z) = 1.1/D(z)$ for redshifts $2.1 < z < 3.5$ when using

quasars for measurements of the autocorrelation of the Ly-α forest and for the cross-correlation between the Ly-α forest and quasars (e.g., Font-Ribera et al. 2014b).

For the $z > 2.1$ BAO projections involving the Ly-α forest, we use the algorithm and code described in Font-Ribera et al. (2014a). For the rest of our forecasts, we use the software GoFish,<sup>114</sup> a Fisher forecast tool for DESI galaxy clustering

<footnote n="114"><sup>114</sup> https://github.com/ladosamushia/GoFish</footnote>
<figure><img src="image_19.png" /><figcaption>**Figure 16.** Left: the forecasted precision on the dilation factor $R$ from DESI BAO measurements compared with the cosmic-variance limit for a 14,000 deg$^2$ survey (black). Right: The forecast precision on $f_{\sigma_8}$ from DESI RSD measurements. In both panels, measurements from each tracer are represented by a different color, and one tracer is assumed over a given redshift range. The redshift range excludes the Ly-$\alpha$ forest measurements for consistency in the illustration of BAO and RSD.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 17.** The assumed central values and predicted uncertainties as a function of wavenumber in the multipole expansion of the power spectrum for each of the discrete tracers in the DESI program. In each case, the red points represent the monopole, the blue points represent the quadrupole, and the green points represent the hexadecapole. The inset panels demonstrate the monopole of the predicted power spectrum relative to a featureless model in order to amplify the BAO feature.</figcaption></figure>

analysis. The forecasts for BAO and RSD precision are based on the projected uncertainties in the clustering measurements. An illustration of the projected precision in the power spectrum for each tracer can be found in Figure 17.

In our Fisher forecast formalism, we include galaxy clustering information depending on the wavenumber interval of focus. From $0.10 < k < 0.50 h \, \text{Mpc}^{-1}$, we only use the information from the BAO feature in the power spectrum to
<figure><img src="image_20.png" /><figcaption>**Figure 16.** Left: the forecasted precision on the dilation factor $R$ from DESI BAO measurements compared with the cosmic-variance limit for a 14,000 deg$^2$ survey (black). Right: The forecast precision on $f_{\sigma_8}$ from DESI RSD measurements. In both panels, measurements from each tracer are represented by a different color, and one tracer is assumed over a given redshift range. The redshift range excludes the Ly-$\alpha$ forest measurements for consistency in the illustration of BAO and RSD.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 17.** The assumed central values and predicted uncertainties as a function of wavenumber in the multipole expansion of the power spectrum for each of the discrete tracers in the DESI program. In each case, the red points represent the monopole, the blue points represent the quadrupole, and the green points represent the hexadecapole. The inset panels demonstrate the monopole of the predicted power spectrum relative to a featureless model in order to amplify the BAO feature.</figcaption></figure>

analysis. The forecasts for BAO and RSD precision are based on the projected uncertainties in the clustering measurements. An illustration of the projected precision in the power spectrum for each tracer can be found in Figure 17.

In our Fisher forecast formalism, we include galaxy clustering information depending on the wavenumber interval of focus. From $0.10 < k < 0.50 h \, \text{Mpc}^{-1}$, we only use the information from the BAO feature in the power spectrum to
<table><caption>**Table 8**
Aggregate Precision on BAO/RSD Measurements and Forecast DETF Figure of Merit</caption><thead><tr><th>Redshift Range</th><th>Design H(z)</th><th>Forecast H(z)</th><th>Design R(z)</th><th>Forecast R(z)</th><th>Forecast fσ<sub>8</sub></th><th>Design FoM</th><th>Forecast FoM (BAO Only)</th><th>Forecast FoM (BAO+RSD)</th></tr></thead><tbody><tr><td>0 &lt; z &lt; 1.1</td><td></td><td>0.62%</td><td>0.28%</td><td>0.24%</td><td>1.56%</td><td></td><td></td><td></td></tr><tr><td>1.1 &lt; z &lt; 1.9</td><td></td><td>0.82%</td><td>0.39%</td><td>0.37%</td><td>1.24%</td><td></td><td></td><td></td></tr><tr><td>1.9 &lt; z &lt; 3.7</td><td>1.05%</td><td>0.88%</td><td></td><td>0.46%</td><td></td><td></td><td></td><td></td></tr><tr><td>0 &lt; z &lt; 3.7</td><td></td><td>0.43%</td><td></td><td>0.18%</td><td>0.95%</td><td>110</td><td>97</td><td>156.8</td></tr><tr><td>0 &lt; z &lt; 2.2</td><td colspan="8">SDSS (Stage-III)</td><td>24</td></tr></tbody></table>

**Note.** We vary spatial curvature as well as dark energy parameters when deriving the FoM values. All cases include Planck CMB temperature and polarization data. All the numbers are for DESI, but we add in the last row the FoM for SDSS to demonstrate a factor of ~8.3 improvement from DESI relative to a single Stage-III experiment paired with Planck CMB temperature and polarization data.

constrain $D_A(z)/r_d$ and $H(z)r_d$. Over larger scales ($0.01 < k < 0.10 h \text{ Mpc}^{-1}$), in addition to the BAO feature information, we make use of the broadband galaxy power by using the power spectrum as a function of wavenumber and angle with respect to the line of sight to constrain $f\sigma_8$. Because the forecasts rely primarily on scales that are much larger than the fiber patrol radius where pairs are less likely to be resolved (Figure 9), we simply rely on the overall number densities and do not forecast uncertainties due to incompleteness on these scales. Future cosmology analyses will introduce algorithms to recover information lost to fiber incompleteness (e.g., Bianchi et al. 2018; Smith et al. 2019; Ross et al. 2020).

To estimate the BAO constraints on $D_A(z)/r_d$ and $H(z)r_d$, we use the approach to isolate the BAO feature described in Hinton et al. (2020). Additionally, to calculate the BAO uncertainties, we assume a degradation of the BAO damping scale following Seo & Eisenstein (2007), with a damping factor of the form

$$A(k, \mu, z) = \exp \left[ -k^2 \left( \frac{(1 - \mu^2) \Sigma_{\perp}^2}{2} + \frac{\mu^2 \Sigma_{\parallel}^2}{2} \right) \right]. \quad (1)$$

Here, the Lagrangian displacement distances are given by $\Sigma_{\perp} = 9.4(\sigma_8(z)/0.9) h^{-1}\text{Mpc}$ and $\Sigma_{\parallel} = \Sigma_{\perp}(1+f(z))$, where both $\Sigma_{\perp}$ and $\Sigma_{\parallel}$ are multiplied by a factor ($\in[0.5, 1]$) to quantify the degradation of the standard BAO reconstruction due to shot noise, following White (2010).

When including the larger scales with RSD information, we assume

$$P(k, \mu, z) = (b(z) + f\mu^2)^2 P_{\text{mass}}(k, z) A(k, \mu, z), \quad (2)$$

where $A(k, \mu, z)$ is given by Equation (1), $b$ is the linear bias parameter (which is marginalized over), and $P_{\text{mass}}(k, z)$ corresponds to the linear mass power spectrum. The covariance matrix used for these Fisher forecasts assumes the linear Kaiser model (i.e., Equation (2) with $A = 1$) and accounts for the shot noise.

It is worth noting that the forecast results obtained for $f\sigma_8$ should be taken with some caution as previous work on spectroscopic surveys showed that the Fisher forecasts for this parameter can be more optimistic compared to the results achieved from the data. Foroozan et al. (2021) showed that the degradation was a result of degeneracies between the geometric parameters and optimistic assumptions about the scale where

information from the linear regime can be extracted. Indeed, Foroozan et al. (2021) found that, when using linear theory, only using scales below $k = 0.08 h^{-1}\text{Mpc}$ in the forecasts resulted in a good match between the forecast and measured $f\sigma_8$ uncertainties in past surveys. In our computation, the cutoff scale is only slightly more optimistic (we use scales up to $k = 0.1 h^{-1}\text{Mpc}$ for the growth rate forecasts), but we account for the potential loss of the information due to nonlinear physics by applying the scale-dependent exponential damping from Equation (1).

While not included in these results, Cuceu et al. (2021) also found a significant gain in information from the anisotropy in the full-shape of Ly-$\alpha$ forest correlations. Their forecasts show that adding this extra information would improve the BAO constraints on $D_A(z)$ and $H(z)$ by a factor of $1.5-1.8$. Therefore, such a measurement could result in significant further improvements of DESI constraints at high redshifts ($z > 2$).

## 6.2. DESI as a Stage-IV Dark Energy Experiment

As explained in Section 2, we designed DESI with the goal to increase the DETF FoM by an order of magnitude beyond Stage-II results and thus qualify as a Stage-IV Dark Energy Experiment. Implicit in the design was that DESI would achieve measurements of the BAO distance scale to a high precision over all redshifts accessible with the BGS, LRG, ELG, and quasar samples. Those design requirements, and the aggregate precision expected from Table 7, are found in Table 8. At redshift intervals $0 < z < 1.1$ and $1.1 < z < 1.9$, the forecasted precision on $R(z)$ is better than the primary science requirement that drove the DESI design. In the highest-redshift interval, accessible primarily through the Ly-$\alpha$ forest, the forecasted precision on $H(z)$ is better than the top-level requirement by almost 20%.

These design requirements were expected to produce cosmological constraints with a DETF FoM of at least 110. Using the predicted precision of the BAO and RSD measurements over all redshifts, we forecast the DETF FoM using the Planck measurements as the only external data set. We also vary the nuisance parameters used within the Planck plik, commander, and SimAll likelihoods (see Planck Collaboration et al. 2020). We assume a cosmological model with time-varying dark energy equation of state parameters and spatial curvature as free parameters in addition to the standard $\Lambda$CDM parameters. As shown in Table 8, we expect to come close to reaching the design goal when using only the BAO data. However, we expect to significantly exceed the design FoM
<table><caption>**Table 8**
Aggregate Precision on BAO/RSD Measurements and Forecast DETF Figure of Merit</caption><thead><tr><th>Redshift Range</th><th>Design H(z)</th><th>Forecast H(z)</th><th>Design R(z)</th><th>Forecast R(z)</th><th>Forecast fσ<sub>8</sub></th><th>Design FoM</th><th>Forecast FoM (BAO Only)</th><th>Forecast FoM (BAO+RSD)</th></tr></thead><tbody><tr><td>0 &lt; z &lt; 1.1</td><td></td><td>0.62%</td><td>0.28%</td><td>0.24%</td><td>1.56%</td><td></td><td></td><td></td></tr><tr><td>1.1 &lt; z &lt; 1.9</td><td></td><td>0.82%</td><td>0.39%</td><td>0.37%</td><td>1.24%</td><td></td><td></td><td></td></tr><tr><td>1.9 &lt; z &lt; 3.7</td><td>1.05%</td><td>0.88%</td><td></td><td>0.46%</td><td></td><td></td><td></td><td></td></tr><tr><td>0 &lt; z &lt; 3.7</td><td></td><td>0.43%</td><td></td><td>0.18%</td><td>0.95%</td><td>110</td><td>97</td><td>156.8</td></tr><tr><td>0 &lt; z &lt; 2.2</td><td colspan="8">SDSS (Stage-III)</td><td>24</td></tr></tbody></table>

**Note.** We vary spatial curvature as well as dark energy parameters when deriving the FoM values. All cases include Planck CMB temperature and polarization data. All the numbers are for DESI, but we add in the last row the FoM for SDSS to demonstrate a factor of ~8.3 improvement from DESI relative to a single Stage-III experiment paired with Planck CMB temperature and polarization data.

constrain $D_A(z)/r_d$ and $H(z)r_d$. Over larger scales ($0.01 < k < 0.10 h \text{ Mpc}^{-1}$), in addition to the BAO feature information, we make use of the broadband galaxy power by using the power spectrum as a function of wavenumber and angle with respect to the line of sight to constrain $f\sigma_8$. Because the forecasts rely primarily on scales that are much larger than the fiber patrol radius where pairs are less likely to be resolved (Figure 9), we simply rely on the overall number densities and do not forecast uncertainties due to incompleteness on these scales. Future cosmology analyses will introduce algorithms to recover information lost to fiber incompleteness (e.g., Bianchi et al. 2018; Smith et al. 2019; Ross et al. 2020).

To estimate the BAO constraints on $D_A(z)/r_d$ and $H(z)r_d$, we use the approach to isolate the BAO feature described in Hinton et al. (2020). Additionally, to calculate the BAO uncertainties, we assume a degradation of the BAO damping scale following Seo & Eisenstein (2007), with a damping factor of the form

$$A(k, \mu, z) = \exp \left[ -k^2 \left( \frac{(1 - \mu^2) \Sigma_{\perp}^2}{2} + \frac{\mu^2 \Sigma_{\parallel}^2}{2} \right) \right]. \quad (1)$$

Here, the Lagrangian displacement distances are given by $\Sigma_{\perp} = 9.4(\sigma_8(z)/0.9) h^{-1}\text{Mpc}$ and $\Sigma_{\parallel} = \Sigma_{\perp}(1+f(z))$, where both $\Sigma_{\perp}$ and $\Sigma_{\parallel}$ are multiplied by a factor ($\in[0.5, 1]$) to quantify the degradation of the standard BAO reconstruction due to shot noise, following White (2010).

When including the larger scales with RSD information, we assume

$$P(k, \mu, z) = (b(z) + f\mu^2)^2 P_{\text{mass}}(k, z) A(k, \mu, z), \quad (2)$$

where $A(k, \mu, z)$ is given by Equation (1), $b$ is the linear bias parameter (which is marginalized over), and $P_{\text{mass}}(k, z)$ corresponds to the linear mass power spectrum. The covariance matrix used for these Fisher forecasts assumes the linear Kaiser model (i.e., Equation (2) with $A = 1$) and accounts for the shot noise.

It is worth noting that the forecast results obtained for $f\sigma_8$ should be taken with some caution as previous work on spectroscopic surveys showed that the Fisher forecasts for this parameter can be more optimistic compared to the results achieved from the data. Foroozan et al. (2021) showed that the degradation was a result of degeneracies between the geometric parameters and optimistic assumptions about the scale where

information from the linear regime can be extracted. Indeed, Foroozan et al. (2021) found that, when using linear theory, only using scales below $k = 0.08 h^{-1}\text{Mpc}$ in the forecasts resulted in a good match between the forecast and measured $f\sigma_8$ uncertainties in past surveys. In our computation, the cutoff scale is only slightly more optimistic (we use scales up to $k = 0.1 h^{-1}\text{Mpc}$ for the growth rate forecasts), but we account for the potential loss of the information due to nonlinear physics by applying the scale-dependent exponential damping from Equation (1).

While not included in these results, Cuceu et al. (2021) also found a significant gain in information from the anisotropy in the full-shape of Ly-$\alpha$ forest correlations. Their forecasts show that adding this extra information would improve the BAO constraints on $D_A(z)$ and $H(z)$ by a factor of $1.5-1.8$. Therefore, such a measurement could result in significant further improvements of DESI constraints at high redshifts ($z > 2$).

## 6.2. DESI as a Stage-IV Dark Energy Experiment

As explained in Section 2, we designed DESI with the goal to increase the DETF FoM by an order of magnitude beyond Stage-II results and thus qualify as a Stage-IV Dark Energy Experiment. Implicit in the design was that DESI would achieve measurements of the BAO distance scale to a high precision over all redshifts accessible with the BGS, LRG, ELG, and quasar samples. Those design requirements, and the aggregate precision expected from Table 7, are found in Table 8. At redshift intervals $0 < z < 1.1$ and $1.1 < z < 1.9$, the forecasted precision on $R(z)$ is better than the primary science requirement that drove the DESI design. In the highest-redshift interval, accessible primarily through the Ly-$\alpha$ forest, the forecasted precision on $H(z)$ is better than the top-level requirement by almost 20%.

These design requirements were expected to produce cosmological constraints with a DETF FoM of at least 110. Using the predicted precision of the BAO and RSD measurements over all redshifts, we forecast the DETF FoM using the Planck measurements as the only external data set. We also vary the nuisance parameters used within the Planck plik, commander, and SimAll likelihoods (see Planck Collaboration et al. 2020). We assume a cosmological model with time-varying dark energy equation of state parameters and spatial curvature as free parameters in addition to the standard $\Lambda$CDM parameters. As shown in Table 8, we expect to come close to reaching the design goal when using only the BAO data. However, we expect to significantly exceed the design FoM
<figure><img src="image_21.png" /><figcaption>**Figure 18.** Relative improvement in 68% confidence intervals over SDSS + Planck expected when constraining the standard ΛCDM parameters ($\Omega_{\Lambda}$, $H_0$, $\sigma_8$) along with the extension parameters ($\Omega_k$, $w_0$, $w_a$) using DESI + Planck.</figcaption></figure>

when adding the RSD measurements. The slight discrepancy between the design FoM and the forecast FoM using only BAO arises from different assumptions about the CMB constraints. At the time that the final design report was completed, we had to rely on forecasts for Planck cosmological results, as opposed to the final Planck results that we use here. For comparison, we also provide in the last row the FoM for SDSS. The large improvement in DESI relative to the Stage-III SDSS program is as expected from a Stage-IV experiment when all Planck constraints are treated equally in the comparison.

### 6.3. Predicted Cosmology Constraints

For our predictions of the final cosmological constraints from DESI, we make use of the full suite of BAO and RSD forecasts found in Table 7. We use the publicly available code Cobaya (Torrado & Lewis 2021) to fit the parameters to the data and infer their posterior distribution.

The constraints are presented for an extension to the standard ΛCDM parameters where we vary the curvature density parameter, $\Omega_k$, and a time-evolving equation of state for dark energy, ($w_0-w_a$). This model is denoted $\omega_0w_a$ cold dark matter (CDM) as done in the DETF paper (Albrecht et al. 2006). We also provide constraints for $w_0$ and $w_p$ since the latter is decorrelated from $w_a$.

As a baseline to assess the advances we expect from DESI, we compute the constraints on the models using DESI and Planck data (Planck Collaboration et al. 2020) and compare them with those from SDSS and Planck. As shown in Figure 18, we expect significant gains across the full parameter space compared to SDSS. The largest of these gains appear in the projected constraints on $\sigma_8$ and $w_p$, demonstrating DESI's power to both constrain growth of structure and the equation of state for dark energy over a wide redshift range. Relative to the SDSS and Planck results, we expect an improvement of a factor of ~6.5 in the DETF FoM for the $\omega_0w_a$ CDM model, as shown in Table 8.

## 7. Conclusion

The SV data demonstrate that the target selection from legacy imaging data and spectroscopy from the DESI instrument on the Mayall Telescope will exceed initial

expectations. In times when the survey speed ranges between $1/6$ and $2/5$, the 854 deg$^{-2}$ sample of BGS Bright targets will provide 647 deg$^{-2}$ spectroscopically confirmed galaxies over the interval $0 < z < 0.4$. In times with higher survey speeds, the LRG sample will produce 478 good redshifts per square degree over the redshift range $0.4 < z < 1.1$; the ELG sample will produce 452 deg$^{-2}$ over $1.1 < z < 1.6$, and quasars at a density of 112 deg$^{-2}$ at higher redshifts, almost evenly split between direct tracers at $1.6 < z < 2.1$ and Lyman-$\alpha$ forest quasars at $2.1 < z < 3.5$. The first year of observations are complete and progressing as expected from the survey simulations.

At the current rate of observing progress, DESI is expected to complete its full footprint covering 14,900 deg$^2$. The central 14,000 deg$^2$ of this area is used to forecast the precision of cosmology measurements. In these forecasts, we expect to reach a cumulative precision of 0.28% on the isotropic BAO distance scale and 1.56% on $f\sigma_8$ from the BGS and LRG samples at redshifts $z < 1.1$. Over the interval $1.1 < z < 1.9$, the ELG and quasar samples are expected to allow BAO measurements at 0.37% precision and RSD measurements of $f\sigma_8$ to 1.24% precision. Finally, at the highest redshifts, we expect to reach a precision of 0.88% on $H(z)r_d$ and 0.91% precision on $D_A(z)/r_d$ using the BAO feature measured in the Ly-$\alpha$ forest relative to the sound horizon. The Ly-$\alpha$ forest measurements will take advantage of both the Ly-$\alpha$ autocorrelation and the Ly-$\alpha$—quasar cross-correlation measurements.

In combining these measurements with information from Planck CMB measurements, these BAO and RSD measurements are forecast to provide dark energy constraints that correspond to a DETF FoM exceeding 150, thus qualifying DESI as a Stage-IV dark energy experiment. When including additional information from lensing and SNe Ia, we expect an even more significant improvement in cosmological precision relative to Stage-II programs.

This paper is one of a series of results reporting the properties of the DESI MWS, BGS, LRG, ELG, and quasar target samples. These papers constitute the first key measurements from the DESI spectroscopic sample. The first year sample completed in 2022 June, and will provide the next series of key measurements from the DESI collaboration. Just as the SV sample was used to confirm the one-point statistics for clustering studies, this first year sample will be used to test whether the DESI samples will meet expectations for BAO and RSD measurements. The DESI collaboration has established five key projects toward this goal, all of which are well underway.

The first of these key projects is focused on the creation of the catalogs and the two-point statistics for each tracer. Similar to those in BOSS (Reid et al. 2016) and eBOSS (Ross et al. 2020), these catalogs will provide data samples corrected for observational systematic errors and a distribution of random positions and redshifts to convey the angular and radial coverage of the survey. The two-point statistics from these catalogs will be presented in both configuration space and Fourier space, with a full characterization of the covariance between data points. Work in support of this key project has already begun with studies of angular systematic errors (e.g., Kitanidis et al. 2020; Chaussidon et al. 2022), clustering properties (e.g., Zhou et al. 2021; Zarrouk et al. 2022), radial systematic errors, redshift classification, and fiber assignment corrections (e.g., Bianchi et al. 2018; Smith et al. 2019). Another key element to this effort will be the N-body
<figure><img src="image_22.png" /><figcaption>**Figure 18.** Relative improvement in 68% confidence intervals over SDSS + Planck expected when constraining the standard ΛCDM parameters ($\Omega_{\Lambda}$, $H_0$, $\sigma_8$) along with the extension parameters ($\Omega_k$, $w_0$, $w_a$) using DESI + Planck.</figcaption></figure>

when adding the RSD measurements. The slight discrepancy between the design FoM and the forecast FoM using only BAO arises from different assumptions about the CMB constraints. At the time that the final design report was completed, we had to rely on forecasts for Planck cosmological results, as opposed to the final Planck results that we use here. For comparison, we also provide in the last row the FoM for SDSS. The large improvement in DESI relative to the Stage-III SDSS program is as expected from a Stage-IV experiment when all Planck constraints are treated equally in the comparison.

### 6.3. Predicted Cosmology Constraints

For our predictions of the final cosmological constraints from DESI, we make use of the full suite of BAO and RSD forecasts found in Table 7. We use the publicly available code Cobaya (Torrado & Lewis 2021) to fit the parameters to the data and infer their posterior distribution.

The constraints are presented for an extension to the standard ΛCDM parameters where we vary the curvature density parameter, $\Omega_k$, and a time-evolving equation of state for dark energy, ($w_0-w_a$). This model is denoted $\omega_0w_a$ cold dark matter (CDM) as done in the DETF paper (Albrecht et al. 2006). We also provide constraints for $w_0$ and $w_p$ since the latter is decorrelated from $w_a$.

As a baseline to assess the advances we expect from DESI, we compute the constraints on the models using DESI and Planck data (Planck Collaboration et al. 2020) and compare them with those from SDSS and Planck. As shown in Figure 18, we expect significant gains across the full parameter space compared to SDSS. The largest of these gains appear in the projected constraints on $\sigma_8$ and $w_p$, demonstrating DESI's power to both constrain growth of structure and the equation of state for dark energy over a wide redshift range. Relative to the SDSS and Planck results, we expect an improvement of a factor of ~6.5 in the DETF FoM for the $\omega_0w_a$ CDM model, as shown in Table 8.

## 7. Conclusion

The SV data demonstrate that the target selection from legacy imaging data and spectroscopy from the DESI instrument on the Mayall Telescope will exceed initial

expectations. In times when the survey speed ranges between $1/6$ and $2/5$, the 854 deg$^{-2}$ sample of BGS Bright targets will provide 647 deg$^{-2}$ spectroscopically confirmed galaxies over the interval $0 < z < 0.4$. In times with higher survey speeds, the LRG sample will produce 478 good redshifts per square degree over the redshift range $0.4 < z < 1.1$; the ELG sample will produce 452 deg$^{-2}$ over $1.1 < z < 1.6$, and quasars at a density of 112 deg$^{-2}$ at higher redshifts, almost evenly split between direct tracers at $1.6 < z < 2.1$ and Lyman-$\alpha$ forest quasars at $2.1 < z < 3.5$. The first year of observations are complete and progressing as expected from the survey simulations.

At the current rate of observing progress, DESI is expected to complete its full footprint covering 14,900 deg$^2$. The central 14,000 deg$^2$ of this area is used to forecast the precision of cosmology measurements. In these forecasts, we expect to reach a cumulative precision of 0.28% on the isotropic BAO distance scale and 1.56% on $f\sigma_8$ from the BGS and LRG samples at redshifts $z < 1.1$. Over the interval $1.1 < z < 1.9$, the ELG and quasar samples are expected to allow BAO measurements at 0.37% precision and RSD measurements of $f\sigma_8$ to 1.24% precision. Finally, at the highest redshifts, we expect to reach a precision of 0.88% on $H(z)r_d$ and 0.91% precision on $D_A(z)/r_d$ using the BAO feature measured in the Ly-$\alpha$ forest relative to the sound horizon. The Ly-$\alpha$ forest measurements will take advantage of both the Ly-$\alpha$ autocorrelation and the Ly-$\alpha$—quasar cross-correlation measurements.

In combining these measurements with information from Planck CMB measurements, these BAO and RSD measurements are forecast to provide dark energy constraints that correspond to a DETF FoM exceeding 150, thus qualifying DESI as a Stage-IV dark energy experiment. When including additional information from lensing and SNe Ia, we expect an even more significant improvement in cosmological precision relative to Stage-II programs.

This paper is one of a series of results reporting the properties of the DESI MWS, BGS, LRG, ELG, and quasar target samples. These papers constitute the first key measurements from the DESI spectroscopic sample. The first year sample completed in 2022 June, and will provide the next series of key measurements from the DESI collaboration. Just as the SV sample was used to confirm the one-point statistics for clustering studies, this first year sample will be used to test whether the DESI samples will meet expectations for BAO and RSD measurements. The DESI collaboration has established five key projects toward this goal, all of which are well underway.

The first of these key projects is focused on the creation of the catalogs and the two-point statistics for each tracer. Similar to those in BOSS (Reid et al. 2016) and eBOSS (Ross et al. 2020), these catalogs will provide data samples corrected for observational systematic errors and a distribution of random positions and redshifts to convey the angular and radial coverage of the survey. The two-point statistics from these catalogs will be presented in both configuration space and Fourier space, with a full characterization of the covariance between data points. Work in support of this key project has already begun with studies of angular systematic errors (e.g., Kitanidis et al. 2020; Chaussidon et al. 2022), clustering properties (e.g., Zhou et al. 2021; Zarrouk et al. 2022), radial systematic errors, redshift classification, and fiber assignment corrections (e.g., Bianchi et al. 2018; Smith et al. 2019). Another key element to this effort will be the N-body
simulations to test theoretical models and mock catalogs to approximate the program at a very large volume. A series of numerical simulations have been compared at the halo level to assess the robustness of numerical simulation methods (Grove et al. 2022), while new techniques have been developed to suppress the effects of sample variance in these N-body simulations using approximate mocks (Ding et al. 2022). New high-fidelity mock galaxy catalogs have also been developed with mass resolution sufficient to resolve dark matter subhaloes for the BGS sample (Safonova et al. 2021), while various techniques have been developed to produce mock catalogs over volumes much larger than possible with N-body simulations (Balaguera-Antolínez et al. 2023).

The remaining key projects relate to the BAO measurements, RSD measurements, and cosmology constraints that will define DESI as a Stage-IV dark energy experiment. The collaboration is now developing the BAO and RSD analyses for the BGS, LRG, ELG, and quasar samples on early data and on blinded catalogs. Effort includes assessment of reconstruction methods, BAO and RSD fitting procedures, and systematic error calculation. At higher redshift, quasars will be used to determine the BAO distance scale through autocorrelation in the Lyman-α forest and cross-correlation between the Lyman-α forest and quasars. First results toward these Lyman-α forest studies include generation of mock catalogs (Farr et al. 2020b), application of a convolutional neural network to characterize damped Lyman-α systems (Wang et al. 2022), a Lyα catalog (Ramírez-Pérez et al. 2023), and a study on the effect of quasar redshift errors on Lyman-α forest correlation functions (Youles et al. 2022; A. Bault et al. 2023, in preparation; García et al. 2023). Finally, the cosmological constraints from the first year measurements will be computed using many of the same tools as those used to make the forecasts in Section 6.

We expect to obtain redshifts for 7.2 million unique stars, 36.12 million unique galaxies, and 2.87 million unique quasars over the main 14,000 deg² spectroscopic footprint. The imaging data for these targets are already being used to constrain the BAO distance scale (e.g., Sridhar et al. 2020; Zarrouk et al. 2021) and growth of structure through cross-correlations with the CMB (e.g., Hang et al. 2021; Kitanidis & White 2021; White et al. 2022). On smaller scales, the spectra will be used for direct constraints on neutrino mass through the one-dimensional Lyman-α forest power spectrum (e.g., Karaçaylı et al. 2022; Göksel Karaçaylı et al. 2023; Ravoux et al. 2023), while, on the largest scales, the catalogs will be used to constrain non-Gaussianity in the primordial density field (e.g., Mueller et al. 2022). Beyond cosmology, DESI will provide spectroscopy to complement imaging from the Vera Rubin Observatory, provide new insights into galaxy evolution, and provide maps of the Milky Way and its neighbors (Dey et al. 2023) that can be used to infer its merger history, density profile, and other evolutionary characteristics. When complete, the DESI program will offer the premier spectroscopic samples for cosmology and astrophysics.

## Acknowledgments

This material is based upon work supported by the U.S. Department of Energy (DOE), Office of Science, Office of High-Energy Physics, under contract No. DE-AC02-05CH11231, and by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract.

Additional support for DESI was provided by the U.S. National Science Foundation (NSF), Division of Astronomical Sciences under contract No. AST-0950945 to the NSF's National Optical-Infrared Astronomy Research Laboratory; the Science and Technology Facilities Council of the United Kingdom; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; the French Alternative Energies and Atomic Energy Commission (CEA); the National Council of Science and Technology of Mexico (CONACYT); the Ministry of Science and Innovation of Spain (MICINN), and by the DESI Member Institutions: https://desi.lbl.gov/collaborating-institutions. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. National Science Foundation, the U.S. Department of Energy, or any of the listed funding agencies.

The authors are honored to be permitted to conduct scientific research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation.

## Data Availability

The Data Release 9 of the DESI Legacy Imaging Surveys is available at https://legacysurvey.org/dr9/.

Documentation of DESI data access is maintained at https://data.desi.lbl.gov/doc/access/.

All data points used in published graphs are available in Zenodo: doi: [doi:10.5281/zenodo.10063934].

## ORCID iDs

S. Ahlen https://orcid.org/0000-0001-6098-7247

S. Alam https://orcid.org/0000-0002-3757-6359

D. M. Alexander https://orcid.org/0000-0002-5896-6313

A. Anand https://orcid.org/0000-0003-2923-1585

F. Andrade-Oliveira https://orcid.org/0000-0003-0171-0069

E. Armengaud https://orcid.org/0000-0001-7600-5148

J. Asorey https://orcid.org/0000-0002-6211-499X

S. Avila https://orcid.org/0000-0001-5043-3662

A. Aviles https://orcid.org/0000-0001-5998-3986

S. Bailey https://orcid.org/0000-0003-4162-6619

A. Balaguera-Antolínez https://orcid.org/0000-0001-5028-3035

O. Ballester https://orcid.org/0000-0002-7126-5300

A. Bault https://orcid.org/0000-0002-9964-1005

S. F. Beltran https://orcid.org/0000-0001-6324-4019

S. BenZvi https://orcid.org/0000-0001-5537-4710

L. Beraldo e Silva https://orcid.org/0000-0002-0740-1507

A. Berti https://orcid.org/0000-0003-3582-6649

F. Beutler https://orcid.org/0000-0003-0467-5438

D. Bianchi https://orcid.org/0000-0001-9712-0006

C. Blake https://orcid.org/0000-0002-5423-5919

R. Blum https://orcid.org/0000-0002-8622-4237

A. S. Bolton https://orcid.org/0000-0002-9836-603X

S. Brieden https://orcid.org/0000-0003-3896-9215

A. Brodzeller https://orcid.org/0000-0002-8934-0954

Z. Cai https://orcid.org/0000-0001-8467-6478

A. Carnero Rosell https://orcid.org/0000-0003-3044-5150

F. J. Castander https://orcid.org/0000-0001-7316-4573

J. L. Cervantes-Cota https://orcid.org/0000-0002-3057-6786

S. Chabanier https://orcid.org/0000-0002-5692-5243

E. Chaussidon https://orcid.org/0000-0001-8996-4874
simulations to test theoretical models and mock catalogs to approximate the program at a very large volume. A series of numerical simulations have been compared at the halo level to assess the robustness of numerical simulation methods (Grove et al. 2022), while new techniques have been developed to suppress the effects of sample variance in these N-body simulations using approximate mocks (Ding et al. 2022). New high-fidelity mock galaxy catalogs have also been developed with mass resolution sufficient to resolve dark matter subhaloes for the BGS sample (Safonova et al. 2021), while various techniques have been developed to produce mock catalogs over volumes much larger than possible with N-body simulations (Balaguera-Antolínez et al. 2023).

The remaining key projects relate to the BAO measurements, RSD measurements, and cosmology constraints that will define DESI as a Stage-IV dark energy experiment. The collaboration is now developing the BAO and RSD analyses for the BGS, LRG, ELG, and quasar samples on early data and on blinded catalogs. Effort includes assessment of reconstruction methods, BAO and RSD fitting procedures, and systematic error calculation. At higher redshift, quasars will be used to determine the BAO distance scale through autocorrelation in the Lyman-α forest and cross-correlation between the Lyman-α forest and quasars. First results toward these Lyman-α forest studies include generation of mock catalogs (Farr et al. 2020b), application of a convolutional neural network to characterize damped Lyman-α systems (Wang et al. 2022), a Lyα catalog (Ramírez-Pérez et al. 2023), and a study on the effect of quasar redshift errors on Lyman-α forest correlation functions (Youles et al. 2022; A. Bault et al. 2023, in preparation; García et al. 2023). Finally, the cosmological constraints from the first year measurements will be computed using many of the same tools as those used to make the forecasts in Section 6.

We expect to obtain redshifts for 7.2 million unique stars, 36.12 million unique galaxies, and 2.87 million unique quasars over the main 14,000 deg² spectroscopic footprint. The imaging data for these targets are already being used to constrain the BAO distance scale (e.g., Sridhar et al. 2020; Zarrouk et al. 2021) and growth of structure through cross-correlations with the CMB (e.g., Hang et al. 2021; Kitanidis & White 2021; White et al. 2022). On smaller scales, the spectra will be used for direct constraints on neutrino mass through the one-dimensional Lyman-α forest power spectrum (e.g., Karaçaylı et al. 2022; Göksel Karaçaylı et al. 2023; Ravoux et al. 2023), while, on the largest scales, the catalogs will be used to constrain non-Gaussianity in the primordial density field (e.g., Mueller et al. 2022). Beyond cosmology, DESI will provide spectroscopy to complement imaging from the Vera Rubin Observatory, provide new insights into galaxy evolution, and provide maps of the Milky Way and its neighbors (Dey et al. 2023) that can be used to infer its merger history, density profile, and other evolutionary characteristics. When complete, the DESI program will offer the premier spectroscopic samples for cosmology and astrophysics.

## Acknowledgments

This material is based upon work supported by the U.S. Department of Energy (DOE), Office of Science, Office of High-Energy Physics, under contract No. DE-AC02-05CH11231, and by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract.

Additional support for DESI was provided by the U.S. National Science Foundation (NSF), Division of Astronomical Sciences under contract No. AST-0950945 to the NSF's National Optical-Infrared Astronomy Research Laboratory; the Science and Technology Facilities Council of the United Kingdom; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; the French Alternative Energies and Atomic Energy Commission (CEA); the National Council of Science and Technology of Mexico (CONACYT); the Ministry of Science and Innovation of Spain (MICINN), and by the DESI Member Institutions: https://desi.lbl.gov/collaborating-institutions. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. National Science Foundation, the U.S. Department of Energy, or any of the listed funding agencies.

The authors are honored to be permitted to conduct scientific research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation.

## Data Availability

The Data Release 9 of the DESI Legacy Imaging Surveys is available at https://legacysurvey.org/dr9/.

Documentation of DESI data access is maintained at https://data.desi.lbl.gov/doc/access/.

All data points used in published graphs are available in Zenodo: doi: [doi:10.5281/zenodo.10063934].

## ORCID iDs

S. Ahlen https://orcid.org/0000-0001-6098-7247

S. Alam https://orcid.org/0000-0002-3757-6359

D. M. Alexander https://orcid.org/0000-0002-5896-6313

A. Anand https://orcid.org/0000-0003-2923-1585

F. Andrade-Oliveira https://orcid.org/0000-0003-0171-0069

E. Armengaud https://orcid.org/0000-0001-7600-5148

J. Asorey https://orcid.org/0000-0002-6211-499X

S. Avila https://orcid.org/0000-0001-5043-3662

A. Aviles https://orcid.org/0000-0001-5998-3986

S. Bailey https://orcid.org/0000-0003-4162-6619

A. Balaguera-Antolínez https://orcid.org/0000-0001-5028-3035

O. Ballester https://orcid.org/0000-0002-7126-5300

A. Bault https://orcid.org/0000-0002-9964-1005

S. F. Beltran https://orcid.org/0000-0001-6324-4019

S. BenZvi https://orcid.org/0000-0001-5537-4710

L. Beraldo e Silva https://orcid.org/0000-0002-0740-1507

A. Berti https://orcid.org/0000-0003-3582-6649

F. Beutler https://orcid.org/0000-0003-0467-5438

D. Bianchi https://orcid.org/0000-0001-9712-0006

C. Blake https://orcid.org/0000-0002-5423-5919

R. Blum https://orcid.org/0000-0002-8622-4237

A. S. Bolton https://orcid.org/0000-0002-9836-603X

S. Brieden https://orcid.org/0000-0003-3896-9215

A. Brodzeller https://orcid.org/0000-0002-8934-0954

Z. Cai https://orcid.org/0000-0001-8467-6478

A. Carnero Rosell https://orcid.org/0000-0003-3044-5150

F. J. Castander https://orcid.org/0000-0001-7316-4573

J. L. Cervantes-Cota https://orcid.org/0000-0002-3057-6786

S. Chabanier https://orcid.org/0000-0002-5692-5243

E. Chaussidon https://orcid.org/0000-0001-8996-4874
J. Chaves-Montero https://orcid.org/0000-0002-9553-4261

C. Chuang https://orcid.org/0000-0002-3882-078X

S. Cole https://orcid.org/0000-0002-5954-7903

A. P. Cooper https://orcid.org/0000-0001-8274-158X

A. Cuceu https://orcid.org/0000-0002-2169-0595

T. M. Davis https://orcid.org/0000-0002-4213-8783

K. Dawson https://orcid.org/0000-0002-0553-3805

R. de Belsunce https://orcid.org/0000-0003-3660-4028

R. de la Cruz https://orcid.org/0000-0001-9908-9129

A. de la Macorra https://orcid.org/0000-0002-1769-1640

J. DeRose https://orcid.org/0000-0002-0728-0960

A. Dey https://orcid.org/0000-0002-4928-4003

B. Dey https://orcid.org/0000-0002-5665-7912

G. Dhungana https://orcid.org/0000-0002-5402-1216

Z. Ding https://orcid.org/0000-0002-3369-3718

K. Douglass https://orcid.org/0000-0002-9540-546X

D. J. Eisenstein https://orcid.org/0000-0002-2929-3121

S. Escoffier https://orcid.org/0000-0002-2847-7498

X. Fan https://orcid.org/0000-0003-3310-0131

K. Fanning https://orcid.org/0000-0003-2371-3356

V. A. Fawcett https://orcid.org/0000-0003-1251-532X

S. Ferraro https://orcid.org/0000-0003-4992-7854

J. Ereza https://orcid.org/0000-0002-0194-4017

A. Font-Ribera https://orcid.org/0000-0002-3033-7312

D. Forero-Sánchez https://orcid.org/0000-0001-5957-332X

J. E. Forero-Romero https://orcid.org/0000-0002-2890-3725

C. S. Frenk https://orcid.org/0000-0002-2338-716X

B. T. Gänsicke https://orcid.org/0000-0002-2761-3005

L. Á. García https://orcid.org/0000-0003-1235-794X

J. García-Bellido https://orcid.org/0000-0002-9370-8360

C. Garcia-Quintero https://orcid.org/0000-0003-1481-4294

L. H. Garrison https://orcid.org/0000-0002-9853-5673

S. Gontcho A Gontcho https://orcid.org/0000-0003-3142-233X

A. X. Gonzalez-Morales https://orcid.org/0000-0003-4089-6924

V. Gonzalez-Perez https://orcid.org/0000-0001-9938-2755

O. Graur https://orcid.org/0000-0002-4391-6137

D. Green https://orcid.org/0000-0002-0676-3661

B. Hadzhiyska https://orcid.org/0000-0002-2312-3121

C. Hahn https://orcid.org/0000-0003-1197-0902

J. J. Han https://orcid.org/0000-0002-6800-5778

M. M. S Hanif https://orcid.org/0009-0006-2583-5006

H. K. Herrera-Alcantar https://orcid.org/0000-0002-9136-9609

C. Howlett https://orcid.org/0000-0002-1081-9410

D. Huterer https://orcid.org/0000-0001-6558-0112

V. Iršič https://orcid.org/0000-0002-5445-461X

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I. Pérez-Ràfols https://orcid.org/0000-0001-6979-0125

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V. Ruhlmann-Kleider https://orcid.org/0009-0000-6063-6121

C. G. Sabiu https://orcid.org/0000-0002-5513-5303

K. Said https://orcid.org/0000-0002-1809-6325

A. Saintonge https://orcid.org/0000-0003-4357-3450

L. Samushia https://orcid.org/0000-0002-1609-5687

E. Sanchez https://orcid.org/0000-0002-9646-8198

C. Saulder https://orcid.org/0000-0002-0408-5633

E. Schaan https://orcid.org/0000-0002-4619-8927

E. F. Schlafly https://orcid.org/0000-0002-3569-7421

D. Schlegel https://orcid.org/0000-0002-5042-5088
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A. Shafieloo https://orcid.org/0000-0001-6815-0337

R. Sharples https://orcid.org/0000-0003-3449-8583

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M. Siudek https://orcid.org/0000-0002-2949-2155

A. Smith https://orcid.org/0000-0002-3712-6892

Z. Sun https://orcid.org/0000-0002-8246-7792

G. Tarlé https://orcid.org/0000-0003-1704-0781

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D. Valcin https://orcid.org/0000-0003-0129-0620

F. Valdes https://orcid.org/0000-0001-5567-1301

M. Valluri https://orcid.org/0000-0002-6257-2341

M. Vargas-Magaña https://orcid.org/0000-0003-3841-1836

A. Variu https://orcid.org/0000-0001-8615-602X

L. Verde https://orcid.org/0000-0003-2601-8770

M. Walther https://orcid.org/0000-0002-1748-3745

B. Wang https://orcid.org/0000-0003-4877-1659

M. S. Wang https://orcid.org/0000-0002-2652-4043

N. Weaverdyck https://orcid.org/0000-0001-9382-5199

R. H. Wechsler https://orcid.org/0000-0003-2229-011X

J. Yang https://orcid.org/0000-0001-5287-4242

C. Yèche https://orcid.org/0000-0001-5146-8533

S. Yuan https://orcid.org/0000-0002-5992-7586

H. Zhang https://orcid.org/0000-0001-6847-5254

C. Zhao https://orcid.org/0000-0002-1991-7295

Z. Zheng https://orcid.org/0000-0003-1887-6732

R. Zhou https://orcid.org/0000-0001-5381-4372

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S. Zou https://orcid.org/0000-0002-3983-6484

Y. Zu https://orcid.org/0000-0001-6966-6925

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A. Shafieloo https://orcid.org/0000-0001-6815-0337

R. Sharples https://orcid.org/0000-0003-3449-8583

W. Sheu https://orcid.org/0000-0003-1889-0227

J. Silber https://orcid.org/0000-0002-3461-0320

F. Sinigaglia https://orcid.org/0000-0002-0639-8043

M. Siudek https://orcid.org/0000-0002-2949-2155

A. Smith https://orcid.org/0000-0002-3712-6892

Z. Sun https://orcid.org/0000-0002-8246-7792

G. Tarlé https://orcid.org/0000-0003-1704-0781

L. A. Ureña-López https://orcid.org/0000-0001-9752-2830

R. Vaisakh https://orcid.org/0009-0001-2732-8431

D. Valcin https://orcid.org/0000-0003-0129-0620

F. Valdes https://orcid.org/0000-0001-5567-1301

M. Valluri https://orcid.org/0000-0002-6257-2341

M. Vargas-Magaña https://orcid.org/0000-0003-3841-1836

A. Variu https://orcid.org/0000-0001-8615-602X

L. Verde https://orcid.org/0000-0003-2601-8770

M. Walther https://orcid.org/0000-0002-1748-3745

B. Wang https://orcid.org/0000-0003-4877-1659

M. S. Wang https://orcid.org/0000-0002-2652-4043

N. Weaverdyck https://orcid.org/0000-0001-9382-5199

R. H. Wechsler https://orcid.org/0000-0003-2229-011X

J. Yang https://orcid.org/0000-0001-5287-4242

C. Yèche https://orcid.org/0000-0001-5146-8533

S. Yuan https://orcid.org/0000-0002-5992-7586

H. Zhang https://orcid.org/0000-0001-6847-5254

C. Zhao https://orcid.org/0000-0002-1991-7295

Z. Zheng https://orcid.org/0000-0003-1887-6732

R. Zhou https://orcid.org/0000-0001-5381-4372

Z. Zhou https://orcid.org/0000-0002-4915-0977

H. Zou https://orcid.org/0000-0002-6684-3997

S. Zou https://orcid.org/0000-0002-3983-6484

Y. Zu https://orcid.org/0000-0001-6966-6925

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