APPLICATION NOTE
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Analytical Evaluation of Signal to Noise
Ratios for SiPM and APD in dToF LiDAR
Applications
AND90257/D
Introduction

Light Detection and Ranging, LiDAR is a critical system
for advanced driver assistance systems, ADAS, andautonomous driving, AD, vehicles, robotic mobility, andindustrial automation. The signal to noise ratio, SNR, of the
LiDAR system is a key parameter that limits the LiDAR
detection probability, particularly at long distances.
The SNR calculation method depends on sensor selection;
this application note presents the analytical calculation of
SNR for SiPM, and for Si and InGaAs APD sensors in a
direct time of flight, dToF LiDAR application.
We analyze SNR for APD−based systems operating at 2
wavelengths, 905 nm and 1550 nm, and a SiPM−based
LiDAR operating at 905 nm.
The LiDAR system specifications employed for the
analysis are typical of today’s Level 2 or Level 3 automotive
systems.
The effect of varying the system optical parameters is also
explored since angular resolution and lens aperture (i.e. lensdiameter) can impact the SNR performance in a different
way depending on sensor choice.

calculated from lens diameter Dlens as Aaperture =p (Dlens 2 / 4), h is target reflectivity, AFoV is the field of viewarea at distance d, which can be calculated as:

ǒAoV2 Ǔ @ tanǒAoV2 Ǔ

F amb. +ŕl)Dlń2

I sun(x)dx(eq. 3)l*Dlń2where l is laser wavelength and Dl is the bandpass filter
width and Isun is spectral solar irradiance. By combining
Eq.1, Eq.2 and Eq.3 the PB. can be calculated as:

ǒAoV2 Ǔ @ tanǒAoV2 Ǔ @ h @ D @P B + 1 @ tan
2
@

ŕ

x

y

2
lens

l)Dlń2l*Dlń2

I sun(x)dx + f (h, AoV, D lens, l, Dl)(eq. 4)

We can observe from above that the background light
power is a function of one condition parameter: target
reflectivity, h, and four design parameters: LiDAR angle ofview, lens diameter, laser wavelength and bandpass filter
width. Famb can also be expressed as a photon rate:
F amb. +F amb.
hcńl(eq. 5)where c is speed of light in vacuum (2.997E8 m/s) and h
is Planck’s constant (6.626E−10 J/Hz). Assuming a fixed h,
AoV and Dlens , the ambient light level at different l may becompared as a function of Dl. From Table 1. we can observethat the 1550 nm system receives 2.6 times lower
background ambient power, however the number of incident
photons per second is only 1.6 times smaller due to thedifference in photon energy between 905 nm and 1550 nm.

Ambient Light Background and Return Signal
Calculations

The background optical power from ambient lightreaching the sensor can be calculated as [1]:1 @Famb. @ A FoV @ h @ e RX @ A aperture
2p @ d 2(eq. 2)where AoVx and AoVy are the sensor horizontal andvertical angle of view, Famb. is ambient light power per unit
area, which can be calculated from the solar irradiancespectrum as:

The following sections provide:
1. Power calculations for light signal and backgroundambient noise
2. The SNR analytical calculation applied to APDs
operating at 905 nm and 1550 nm and to a SiPM
from onsemi at 905 nm. For SiPM the calculations
are verified using waveform simulation
3. Analysis of the effect of sensor choice, opticalparameters, and readout electronics on SNR
4. Discussion of system level design tradeoffs
considering the results of the SNR analysis

PB +

y

x

A FoV + 4d 2 @ tan(eq. 1)

where d is target distance, eRX , is receiver optics
efficiency, Aaperture is receiving lens aperture, which is© Semiconductor Components Industries, LLC, 2023

October, 2023 − Rev. 0

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Table 2. TYPICAL LiDAR SYSTEM SPECIFICATIONSUSED FOR SNR ANALYSIS

Table 1. COMPARISON OF AMBIENT BACKGROUND
POWER IN 905 nm AND 1550 nm SYSTEMS FOR
DIFFERENT BANDPASS FILTER WIDTHS
Famb W/m2

Test System#1

Condition

#2

#3

Dl nm

905 nm1550 nmFamb.(905) /Famb.(1550)

Famb.(905) /Famb.(1550)

FoV (H×V)

6

4.42

1.62

2.72

1.59

AoVx

1°

0.1°

0.05°

10

7.07

2.71

2.61

1.52

AoVy

1°

0.1°

0.05°

20

13.81

5.40

2.56

1.49

eRX

50

37.72

13.27

2.84

1.66

eTX

90 %

1.57

Dlens

from 1 to 50 mml

905 or 1550 nm

Dl

50 nm

tlaser

10 ns

80

56.34

20.81

2.70

Assuming a Lambertian target where the laser spot is
within the sensor AoV and is smaller than the target, theintensity of the return laser pulse at the sensor can becalculated as:

120° × 40°

90 %Nshots1

Plaser100 W(eq. 6)

Target Distance d

50 m, 200 m

where Plaser is the initial laser power and eTX , is emitter
optics efficiency.
To illustrate the relationship between PB , PS and SNR inpractice, a generic LiDAR system is employed. The systemlevel specifications and target performance are presented inTable 2 with three optional values for AoVx and AoVy which
define the system resolution. Dlens is variable such that adifferent optical aperture may be chosen for optimal
performance with the detector and wavelength of choice.
The ambient light flux is set to 100klux, while target
reflectivity is set to 10% as this represents the mostchallenging condition for SNR in the LiDAR application.

Target reflectivity h

10%Ambient Light Flux

100 kLux

PS +

1 @P
laser @ e RX @ e TX @ h @ A aperture
2p @ d 2

Both signal (Eq.6) and background (Eq.4) powers arefunctions of Aaperture = f(Dlens ). Therefore, PB and PS were
calculated for different Dlens values from 1mm up to 50 mm
and plotted in Figure 1 for 200 m and 50 m targets. We canobserve that a system with a larger aperture collects more
return laser light power, PS , however the background power,
PB in such a system is higher too. PB might be decreased,without compromising PS , by reducing the filter bandpass
width, Dl, and sensor angle of view AoVx , AoVy. If Dl, andAoV are otherwise constrained by system design choices, alarge Dlens is recommended for LiDAR systems equippedwith low light sensitivity detector, while for systems
equipped with high light sensitivity a small Dlens size ispreferable.
Signal to Noise Calculation for Si and InGaAs APDs

The Signal to Noise Ratio SNR of an APD−based LiDAR
system can be calculated [2] as:
SNR APD +

Ǹ

2eB n

ǸNshots
F

R 2O

P 2S
B

(R O @ P S ) R O @ P B ) I D) ) N2
M

ǒ

4k BT
R

f

)

tV ampu 2R2fǓ(eq. 7)

where Nshots is the number of dToF measurements per
point, R0 is APD responsivity without multiplication*, e iselectron charge, BN is noise bandwidth (frequency at which
amplifier gain is equal to 0 dB), F is APD excess noise factor,
ID is APD dark current, M is APD multiplication factor or
Gain, T is temperature in K, <Vamp > is amplifier input
voltage noise density and Rf is feedback resistance.
*Typically, the responsivity after multiplication R = R0 x M ispresented in APD datasheets

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Figure 1. Return Laser Power (expressed in percentage and Watts for initial laser power of 150, 100, 50 and 10 W)
as a Function of Background Light Power (expressed in Watts and photons per second) for 905 and 1550 nm
Systems. Results presented at different Dlens and AoV Values and for two Target Distances of 200 m and 50 m.
Table 3. APD (Si AND InGaAs) AND SiPM
PARAMETERS USED FOR SNR CALCULATIONS
APD
l

Si

InGaAsonsemi
SiPM

905 nm1550 nm

905 nm

50 nm

Dl
QE

55 %

72 %

N/A

PDE

N/A

N/A

30%

R0

0.4

0.9

N/A

M or G

100

30

1e6

F

4

7

1.35

ID

50 pA

150 nA

2 pA

DCR

N/A

N/A

1 MHz/mm2

Ncells

N/A

N/A

2400

PXT

N/A

N/A

15%

tdead.

N/A

N/A

14 ns

BN

SNR was calculated for one Si APD at 905 nm and one
InGaAs APD at 1550 nm. The InGaAs APD has smaller
bandgap energy with respect to Si making it sensitive to
longer wavelengths. However, due to shorter bandgap
energy InGaAs devices have higher ID (for the same activearea) compared to Si APDs. Moreover, the Si process ismore advanced and purer than InGaAs which leads to evenlower ID in the Si sensor. ID is an important APD parameter
which limits the maximum APD multiplication, M, which
limits responsivity R=R0 ×M. The Si and InGaAs APD
parameters are listed in Table 3. In the system model it isassumed the APD is connected to a transimpedance
amplifier with noise bandwidth BN = 1 MHz and feedback
resistor Rf of 10 kW.
The SNR as a function of PS and PB for Si and InGaAs
APDs was calculated from Eq.7 and is plotted in Figure 6.
The expected values of PS and PB are plotted for a laser withinitial power of 100 W by white (AoVx y AoVy = 1°×1°), grey
(AoVx y AoVy = 0.1°×0.1°) and black (AoVx y AoVy =0.05°×0.05°) lines, for a target at 200 m distance and withdifferent Dlens from 1 to 50 mm. The locations at which SNR= 10 are highlighted by dashed red lines.

1 MHz

Rf

10 kW

<Vamp>

28 nV/√Hz

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Signal to Noise Calculation for SiPM Device

simulated waveform (black) and overlap of 1000
waveforms together with <AS > and sB is presented in
Figure 2.
The comparison of SNR from analytical calculation (i.e.
Eq.11) and numerical waveform simulation is plotted
Figure 3. We can observe a good agreement between
simulation and analytical calculation at all simulated returnlaser power levels from 200 nW up to uW and backgroundpower levels from 0.1 pW up to nW. There is a small
discrepancy at the lowest PB = 0.1 pW. This difference could
be related to SiPM microcell to microcell gain variation
which is included in the waveform simulation but not in theanalytical calculation.

A SiPM is a parallel array of microcells where eachmicrocell is composed of a Single Photon Avalanche Diode,
SPAD, connected in series with a quenching resistor [3].
Each SiPM microcell works as a binary device producing ashort uniform pulse each time a photon is detected. The
SiPM generates an analog output signal, which is the sum of
signals from all microcells. The SiPM parameters used for
SNR calculation are presented in Table 3.
For SiPM, the detected noise floor can be expressed interms of average number [1] of busy microcells due toambient light:
N amb + N cellsǒȡ@ȧ1 * eȢ*P
B@PDE)DCR
hcńl

Ǔ

ȣ
ȧ
Ȥ

t
dead
N cellsń(1*tXTu)(eq. 8)where PDE is SiPM photon detection efficiency, tdead isdead time and Ncells is number of microcells, DCR is SiPM
dark count rate and <XT> is an average number of crosstalkevents per single avalanche, calculated from SiPM crosstalkprobability PXT as [4]:t XT u+ * ln(1 * P XT)(eq. 9)The detected return laser signal can be calculated as anumber of microcells, Nlaser, firing due to laser photons:ȡȧȢ

N laser + (N cells * N amb) @

1*e

*

ǒ

P
S
@PDE)DCR
hcńl

Ǔ

ȣ
ȧ
Ȥ

t
laser
N cellsń(1*tXTu)

Figure 2. Collection of 1000 SiPM Waveforms
Overlapped, and a Single Waveform (black line),
simulated for PB = 0.05 nW and PS of 10 nW. Signal
amplitude is expressed as number of detected single
photon events (p.e.)(eq. 10)where tlaser is the laser pulse width.
The SNR for SiPM devices can be calculated from thenumber of fired microcells as:
SNR SiPM + ǸN shots

N laserǸNamb ) N 2elec.

(eq. 11)

where Nelec. is the number of microcells occupied due toelectronic noise:
N 2elec. +ǒet GǓ
dead

2

BN

ǒ

4k BT t V amp u 2
)
Rf
R 2f

Ǔ

(eq. 12)The SNR for SiPM, as a function of PS and PB , is plottedin Figure 6 (left).
Validation of Analytical Calculation with Numerical
Simulation

To validate the analytical calculation of SNR for SiPM, anumerical Toy Waveform Simulation was done. At a given
PS and PB 1000 waveforms were simulated, and SNR was
calculated as:
SNR sim. +t AS usB

Figure 3. Comparison of SNR from Analytical
Calculation (solid lines) and Numerical Simulation(dashed lines) under Various Background andReturn Laser Signal Powers(eq. 13)

where <AS > is an average detected laser signal amplitude
and sB is noise standard deviation. An example of one
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Comparison of SNR for SiPM and APD

The SNR for onsemi SiPM and for APDs (Si and InGaAs),
as a function of PS and PB , is plotted in Figure 6.
For comparison, the condition at which SNR = 10 ishighlighted by red solid and dashed lines for SiPM, andAPDs, respectively. The LiDAR detection probability PD
can be calculated for a selected SNR and false alarm rate. For
example, PD = 80% when SNR = 10 and false alarmprobability, Pfa = 0.1% [5]:P D [ 0.5erfcǒǸ* ln(P fa) * ǸSNR ) 0.5Ǔ

(eq. 14)

The expected values of PS and PB are shown for three
LiDAR test systems (Table 2) with variable receiver lensdiameter Dlens .
We can observe that due to its single photon sensitivity the
SiPM requires 14 times less return laser power with respect
to the Si APD and 85 times less return laser power withrespect to the InGaAs APD to achieve a SNR of 10 (SiPM
requires 7×10−11 W, while Si APD needs 10−9 W and
InGaAs 6×10−9 W).
Because of its high photon sensitivity, the onsemi SiPM
is also more sensitive to ambient light. We can observe theeffect of high background on SNR at PB > 10−12W for the
SiPM, while the Si APD can tolerate two orders ofmagnitude higher PB ~10−9 W and the InGaAs APD is
almost insensitive to ambient light level up to 10−7 W.
The SNR for those three systems is plotted in Figure 7. We
can observe for the onsemi SiPM that SNR is limited by thehigh ambient light level when system FoV is 1°×1°. For Test
System #2 with AoVx × AoVy = 0.1°×0.1° the SiPM−based
system outperforms the APD−based system when Rx optics
with small aperture are used (Dlens < 22 mm). Finally, for
Test System #3 with AoVx ×AoVy = 0.05°×0.05° the
SiPM−based system outperforms both APD−based systems
at any aperture (Dlens ).

Figure 4. SNR as a Function of Amplifier Noise
Density for SiPM (left) and Si APD (right)
at Different BN

Figure 5. SNR as a Function of Amplifier Noise
Density for SiPM (left) and Si APD (right)
at Different Rf
SNR and Other LiDAR System Considerations

By comparing Si and InGaAs APD−based LiDAR
systems, we observe that due to its higher internal noise (i.e.,dark current ID ) and relatively low gain, M, the InGaAs
APD requires 5−7 times higher laser power to achieve thesame SNR as the Si APD under the same conditions (optics,
resolution, background, sensor size.).
A system operating at 1550 nm is not constrained by thesame eye safety power limit as a 905 nm system, whichmeans the InGaAs APD−based system can compensate byusing more powerful lasers. However, higher power lasermeans higher power consumption, more heat to bedissipated and, hence more bulky and less economicalsolutions.
Comparing the SNR for Si and InGaAs APDs and onsemi
SiPM, one can observe that due to its single photon
sensitivity the onsemi SiPM requires 14 times less laser
return power to achieve the same SNR as the Si APD and
84 times with respect to the InGaAs APD.
While it is more sensitive to the light signal the SiPM is
also more sensitive to ambient light compared to APDs.
Therefore, the ambient light should be controlled to benefit
from the advantages that the SiPM can provide. The
background light power reaching the sensor can effectively

Effect of Read−out Electronics on SNR

The read−out electronics may affect performance in any
light detection application. This model may also be used toanalyze the effect of amplifier noise density <Vamp > on
SNR. The calculations were performed for SiPM and for Si
APD with various values of feedback resistor Rf and noise
bandwidth BN because those parameters affect the SNR too.
For InGaAs APD the effect is qualitatively similar to Si APD
but quantitively even larger due to smaller M.
The SNR as a function of <Vamp >, calculated for different
BN and Rf is presented in Figure 4 and Figure 5 respectively
for SiPM (left) and Si APD (right). The calculations weredone at PS = 1 nW and PB = 0.07 nW where the SiPM and
Si APD have the same SNR of 14. We can observe that for
both SiPM and Si APD the SNR decreases with increasing<Vamp > however the SiPM can tolerate almost two ordersof magnitude higher <Vamp > at the same BN and Rf thanAPD due to higher internal Gain. Also, in the APD case the
SNR shows much high dependence on BN and Rf , while for
SiPM the SNR is almost independent of BN and Rf provided<Vamp > stays below 10 nV/√Hz.

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be kept within the SiPM’s operating range by using a small
aperture lens and a narrow angular field of view. This is thecase even under the high ambient light conditions that areencountered in automotive LiDAR.
These design solutions align well with existing trends in
LiDAR system requirements i.e. miniaturization (small lensdiameter) and high angular resolution (small angular field ofview per SiPM).
It should be noted that a similar constraint would apply to
the APD if it were to have a dramatically higher
responsivity. In general, a large aperture is recommended
for LiDAR systems equipped with low light sensitivity
detector or detector which could tolerate high ambient
light level, while for systems equipped with high lightsensitivity a small aperture size is preferable.
A third consideration is the increasing use of VCSELs
instead of classic edge−emitting lasers as illuminator. Due tohaving a smaller wavelength shift across operating
temperature the VCSEL enables the use of narrower
bandpass filters on the Rx path, which leads to ambient
light reduction in the spectral regions adjacent to thewavelength of interest.

From Eq.7 and Eq.11 we observe that, independent ofsensor type, SNR~/Nshots . Therefore, in either case, SNR
may be improved by a multi−shot approach, taking
multiple dToF measurements per point in the scene.
Summary and Takeaways

In this analysis we looked at analytical calculation of
Signal to Noise ratio SNR for Si APD, InGaAs APD and
onsemi SiPM sensors. The calculation was verified with anumerical waveform simulation for the SiPM case. We
found that LiDAR systems could significantly benefit fromthe SiPM’s single photon sensitivity and high internal gain
for robust detection of low power return signals.
To realize all the advantages the SiPM could provide theoptical system should be designed to suppress unwanted
interference from ambient background light. In practice thisleads to optical system miniaturization and high angularresolution
Also, due to its much higher internal Gain, the
SiPM−based LiDAR system will tolerate almost two ordersof magnitude higher noise density in the readout chain thanAPD−based systems, without significant SNR degradation,
making the SiPM−based system less dependent on readout
performance, and thus simplifying the readout design task.

From analytical calculation of SNR, we found that due torelatively small internal multiplication M, the choice ofread−out electronics is critical for APD−based LiDAR
system, because the amplifier noise density could
significantly reduce the SNR. To overcome this limitationand simplify the read−out electronics design, an APD withhigh M is required. Unfortunately, M is limited by APD darkcurrent and could not exceed ~ 1k in the best scenario. This
limitation is not a problem for SiPM devices which havemuch higher internal Gain of ~ 106. Such high gain allows
the use of read−out electronics with almost two orders ofmagnitude higher noise density than APD−based systems
can tolerate, without significant SNR degradation.

In conclusion, by utilizing SiPM sensors instead of
APD in 905 nm LiDAR the detection range can beincreased, or the laser power can be reduced while
simplifying readout electronics and optimizing theoptical system, making the SiPM better suited toachieving low cost, low power, and compact LiDAR
solutions.
For more information about SiPM for LiDAR go toonsemi.com/support

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Figure 6. SNR for onsemi SiPM (left), Si APD (middle) and InGaAs APD (right) as a Function of PS and PB . The redlines represent SNR = 10. The expected value of PS and PB for target with η = 10% at 200 m distance, for different
Dlens from 1 to 50 mm, and different AoV are presented by white (AoVx ×AoVy = 1° ×1° ), grey (AoVx ×AoVy =0.1° ×0.1° ) and black (AoVx ×AoVy = 0.05° ×0.05° ) lines. The SNR was limited to 100.

Figure 7. SNR as a Function of Rx Lens Diameter, Dlens , for Three Test Systems (for test system details, refer toTable 2) with different Field of View per channel (i.e. resolution). Results presented for onsemi SiPM (orange),
Si APD (olive) and InGaAs APD (red) (sensor specifications are presented in Table 3). The red dashed line
represents the reference point where SNR = 10.

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References[1] S. Gnecchi and C. Jackson, “A 1 × 16 SiPM Array
for Automotive 3 D Imaging LiDAR Systems,” 2017.
[2] A. Buchner, S. Hadrath, R. Burkard, F. Kolb, J.
Ruskowski, M. Ligges and A. Grabmaier, “Analytical
Evaluation of Signal−to−Noise Ratios for Avalanche−and Single−Photon Avalanche Diodes,” Sensors, vol.
21, p. 2887, 2021.
[3] onsemi, “Introduction to the Silicon Photomultiplier(SiPM) AND9770/D,” 08 2023. [Online]. Available:
https://www.onsemi.com/download/application−notes/p
df/and9770−d.pdf.

[4] S. Vinogradov, “Analytical models of probability
distribution and excess noise factor of Solid State
Photomultiplier signals with crosstalk,” NIM A, vol.
695, 2012.
[5] D. Chu, S. Aboujja and D. Bean, “1550nm triple
junction laser diode for long range LiDAR,”
inproceedings, p. 23, 2022.

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