Optical Engineering 51(11), 111702 (November 2012)

Snapshot advantage: a review of the light collection
improvement for parallel high-dimensional measurement
systems
Nathan Hagen
Rice University
Bioengineering Department
6500 Main Street
Houston, Texas 77005
E-mail: nhagen@optics.arizona.edu
Robert T. Kester
Rebellion Photonics Inc.
7547 South Freeway
Houston, Texas 77021

Abstract. The snapshot advantage is a large increase in light collection
efficiency available to high-dimensional measurement systems thatavoid filtering and scanning. After discussing this advantage in the context
of imaging spectrometry, where the greatest effort towards developing
snapshot systems has been made, we describe the types of measurements where it is applicable. We then generalize it to the larger context
of high-dimensional measurements, where the advantage increases
geometrically with measurement dimensionality. © 2012 Society of Photo-Optical
Instrumentation Engineers (SPIE). [DOI: 10.1117/1.OE.51.11.111702]

Subject terms: snapshot; imaging spectrometry; high-dimensional systems; advantage; throughput.

Liang Gao
Tomasz S. Tkaczyk
Rice University
Bioengineering Department
6500 Main Street
Houston, Texas 77005
E-mail: ttkaczyk@rice.edu

Paper 111429SSR received Nov. 16, 2011; revised manuscript received Feb. 3,
2012; accepted for publication Mar. 19, 2012; published online Jun. 13, 2012.

1 Introduction
Imaging spectrometers collect data over three dimensions—
two spatial ðx; yÞ and one spectral ðλÞ—so that the complete
ðx; y; λÞ dataset is typically referred to as a datacube. The
most common method for categorizing the various typesof imaging spectrometers is by the portion of the datacube
collected in a single detector readout. “Whiskbroom” spectrometers, which use a linear array of detectors, collect asingle column of the datacube at a time and thus scan acrossthe two spatial dimensions of the datacube (see Fig. 1).1
“Pushbroom” spectrometers use a 2D detector array, andthus collect a vertical slice of the datacube at once so that
only one spatial dimension needs to be scanned to fill out
the cube.2 A filtered camera, constructed by placing a filter
wheel or tunable spectral filter in front of a camera, collects ahorizontal slice and thus needs to scan along the spectral
dimension to complete the data set.3 Other scanning modalities exist, such as Fourier Transform imaging spectrometry(FTIS), but these can be shown4,5 as equivalent to one of theabove categories—in this case, the filtered camera.
“Snapshot” imaging spectrometers, in contrast, collect theentire 3D datacube in a single integration period without
scanning. While the existing literature cites advantages forsnapshot instruments such as the lack of scanning artifacts
and the increased robustness or compactness due to thelack of moving components,6 these qualities are actually secondary to the main benefit of snapshot collection, which has
been given little attention. This is the advantage in light collection (optical throughput), which can be dramatic for larger
datacubes. As a parallel to the Jacquinot (throughput) advantage and the Fellgett (multiplex) advantage nomenclature
0091-3286/2012/$25.00 © 2012 SPIE

Optical Engineeringcommonly used in spectrometry, we call this the snapshot
advantage.
While discussion of the light collection advantages ofsnapshot imaging spectrometers has had some exposure in
the astronomy community,7–9 discussion has been limited
to instruments coupled to astronomical telescopes. As aresult, few outside the astronomy community (excepting
only Refs. 10 and 11) are even aware of this important
issue,12 which has not even been given a name. We provide
below the first comprehensive discussion of its characteristics across all modalities.
2 Snapshot Advantage Factor
The snapshot advantage factor is easily derived from knowledge of the datacube dimensions and the measurement
architecture. For example, for a datacube of dimensions
ðN x ; N y ; N λ Þ ¼ ð500; 500; 100Þ, a whiskbroom (point scanning) system sees only 100 voxels of the datacube at any
given time. If the remainder of the object is emitting lightduring this period, then all light emitted outside these 100
voxels is lost. The overall light collection efficiency fromgeometric considerations alone is thus the inverse of thenumber of elements in the scan—in this case 1∕ðN x N y Þ ¼
4 × 10−6 . This value is cripplingly low for all but themost forgiving of experiments. For a pushbroom (line scanning) system, one sees a 500 × 100 slice of the datacube at agiven time, so the maximum full-cube efficiency value is1∕N y ¼ 0.002. While many experiments can tolerate sucha low efficiency, dynamic scenes prevent the longer integration times needed to overcome this poor light collection.
Since the λ scan dimension in our example is one fifth thatof the spatial dimensions, filtered cameras have the potential
to provide a five-fold improvement in light collection ability.
In practice, however, this is typically offset by light losses

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November 2012/Vol. 51(11)Hagen et al.: Snapshot advantage: a review of the improvement in light collection for parallel high-dimensional measurement systems

Fig. 1 The portions of the datacube collected during a single detector integration period for (a) scanning, and (b) snapshot devices.

due to dead time between scan points or to low transmission
in the spectral filters (see, for example, Ref. 13). Ignoringthese losses, the geometric efficiency still remains low, at
1∕N λ ¼ 0.01. These efficiency values given for scanningdevices have been obtained by geometric considerations
alone.
Not all snapshot instruments take advantage of thisimprovement in light collection, however. In terms oflight collection capacity, one can divide snapshot techniques
into two broad categories—“full-throughput” and “throughput-division” techniques—based on whether or not theysacrifice light based on their geometry. That is, although
all snapshot systems remove the need to scan, and thus
do not have the 1∕N efficiency loss associated with scanning
across N elements, throughput-division snapshot implementations suffer from the same light collection tradeoffs as theirscanning counterparts. For example, the multiaperturefiltered camera14–17 [a division of aperture (DoAp) technique,see Fig. 2(a)] consists of an array of mini-cameras eachwith its own spectral filter. The efficiency of each individualmini-camera, however, is reduced to 1∕N λ because of the
bandpass filters used. A second example is the multispectral

Fig. 2 System architectures for snapshot spectral techniques: (a) division of aperture (DoAp) multiaperture filtered camera, and (b) divisionof focal plane (DoFP) the multispectral filter array camera.

Optical Engineeringfilter array camera18,19 [a division of focal plane technique,see Fig. 2(b)]. This system uses a single monolithic lens forlight collection, but places filters over each individual pixelin order to spectrally resolve light in the image. This technique thus sacrifices a 1∕N λ fraction in pixel fill factor, for
any individual wavelength band in the datacube. The fractionof 1∕N λ is thus a fundamental geometric limit to light efficiency for these techniques. Due to the use of filters in bothof these architectures, the light collection efficiency is thus
no better than for equivalent scanning systems.
Full-throughput snapshot techniques, on the other hand,
have no filters, and thus no fundamental geometric tradeoffs
in light collection. There is a remarkable variety of architectures available for full-throughput imaging spectrometers,
among which are (in order of provenance) computed tomographic imaging spectrometry20 (CTIS), fiber-reformatting
imaging spectrometry (FRIS),21,22 integral field spectroscopy
with lenslet arrays23 (IFS-L), integral field spectroscopy withimage slicing mirrors24 (IFS-S), image-replicating imaging
spectrometry11 (IRIS), filter stack spectral decomposition25(FSSD), coded aperture snapshot spectral imaging26(CASSI), image mapping spectrometry27 (IMS), and multispectral Sagnac interferometry28 (MSI). See Fig. 3 for systemlayout diagrams. This list of full-throughput snapshot instruments is steadily increasing, and system designers can evenlook forward to snapshot 3D detector arrays, in which thedetector itself is capable of resolving spectra at individual
pixels.29–33
The convergence of three recent technological advances
has made snapshot imaging spectrometry possible. First is
the steady decrease in cost and pixel size for large format
detector arrays. These enable compact instruments with alarge number of sensing elements with fast readout speed
and reasonable cost. Since typical datacubes have 10 million
or more elements, snapshot techniques require very large
detector arrays in order to properly sample a sufficientnumber of datacube voxels. Only in the past decade havesuch detector arrays become economical. The second technological advance is in the manufacturing tools for making
precision multiaperture optical elements, such as lenslet andmicromirror arrays. These array optical elements allow one
to design compact instruments containing a large number (upto tens of thousands) of parallel optical systems. Finally, the111702-2

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November 2012/Vol. 51(11)Hagen et al.: Snapshot advantage: a review of the improvement in light collection for parallel high-dimensional measurement systems

Fig. 3 System architectures for CTIS, CASSI, IMS, IFS-L, fiber-reformatting imaging spectroscopy (FRIS), and filter stack spectral decomposition(FSSD).

third technological advance, the increased computing power
available to desktop computers, has enabled algorithms thatcan readily display and analyze the large datasets producedby these instruments.
3 Measurements Where the Snapshot
Advantage Applies
The 1∕N values for geometric light collection efficiency
relate directly to signal collection in passive measurement
situations (e.g., remote sensing), in which the user has nocontrol over the illumination source. For active illumination
systems such as microscopes, however, one can compensate
for a low geometric efficiency by illuminating individual
pixels of the object with high intensity laser light, and measuring with a whiskbroom spectrometer. This is the method
used by confocal laser scanning microscopy (CLSM). Using
coherent sources to boost the illumination power density,
however, faces a fundamental limit when the power becomeshigh enough to alter or damage the sample, or, as in fluoOptical Engineeringrescence microscopy, when all fluorophores in the illuminated region have been boosted to their excited state—asituation which is largely achieved in modern confocal
laser scanning microscopes.34 At this point nothing further
can be done on the illumination-side to increase light collection, placing a fundamental limit on overall signal. This isexactly what we have shown in a recent experiment:
while the excitation laser of a CLSM excited the sample
to 0.56 of the theoretical limit, the overall photon collectionof the CLSM remained two orders of magnitude lower thanthat of an equivalent snapshot spectral imaging system,
despite the use of a light source with four orders of magnitude lower power density.34
An active illumination setup also allows one to encode
spectral information into the illumination-side, so that the detection system need not spectrally resolve the image in orderto obtain the ðx; y; λÞ datacube measurement. At this point,
however, we are not aware of a technique allowing this to bedone without throughput loss. Rather, all techniques appear

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November 2012/Vol. 51(11)Hagen et al.: Snapshot advantage: a review of the improvement in light collection for parallel high-dimensional measurement systems

Table 1 Snapshot instruments and their maximum theoretical efficiency values.

Instrument

Date

Efficiencya

DoAp

1991

1∕N λ

Assumes that light from the object uniformly illuminates the system entrance pupil

CTIS

1994

0.3

Computationally intensive, requires a precision-manufactured custom kinoform grating

IFS-L

1995

1

Inefficient use of detector array pixels

FRIS

1995

0.5

Assumes the image is bandlimited to the Nyquist limit of the fiber array; ∼50% light loss between fibersb

IFS-S

1996

1

Requires a precision-manufactured custom micromirror array; allows only low spatial resolution

IRIS

2003

0.5

DoFP

2004

1∕N λ

Probably limited by aberrations to ∼16 spectral channels
pﬃﬃﬃﬃﬃﬃ
Assumes the image is bandlimited to 1∕ N λ times the Nyquist limit in each direction

FSSDc

2004

T Nλ

Probably limited to 4 ∼ 5 spectral channels due to filter losses

CASSI

2007

0.5

Computationally intensive, sensitive to calibration error, assumes that the scene is highly compressible

IMS

2009

1

MSI

2010

0.5

Requires a precision-manufactured custom micromirror array and a precision micro-optical arraypﬃﬃﬃﬃﬃﬃ
Assumes the scene is bandlimited to 1∕ N λ times the Nyquist limit in each direction

Notes

a

Ignores all small factors such as lens transmission and mirror reflectivity.
Bland-Hawthorn et al.43 have shown that this light loss can be reduced to a small amount by carefully fusing multimode fibers.
The throughput of spectral channel n ¼ 0; 1; : : : ; N λ − 1 is given by T 2n for filter transmission T .

bc

to involve either scanning35 or the illumination-side equivalent of the DoAp/DoFP configurations,36 so that the overall
light collection suffers by a factor of 1∕N y or 1∕N λ in comparison to snapshot imaging spectrometers using broadband
illumination.
For remote sensing, on the other hand, the geometric lightcollection efficiency is all-important. Here the user does nothave the ability to manipulate the light source, and almost all
object datacube voxels are continuously emitting light, sothat only a parallel light collection technique can capture
the full signal. For scanning instruments, this setup results
in a tradeoff between light efficiency and the number ofscan elements, a feature which has frustrated the expansionof imaging spectrometry into new fields where there is justnot enough light to permit a tradeoff. These include, forexample, spectral imaging of dynamic objects, target tracking,37 and overcoming signal-to-noise-ratio-limited spectral
unmixing.38–40
The full-throughput snapshot advantage does, however,come at the price of an increase in system complexity, either
in the optical hardware or in the reconstruction software.
Most of the snapshot techniques involve arrays of optical elements, and thus require advanced manufacturing techniquesthat have only recently become available. In addition, withthe exception of CASSI, all of these instruments require large
format detector arrays, and this is perhaps their primary limitation. Detector technology, however, has been advancing at
a pace paralleling that of Moore’s law,41,42 so that we can
expect these limitations to ease in the coming years, both interms of the overall pixel count, cost per pixel, and pixel
readout speed.
One may argue that the complexity tradeoff compromises
the snapshot advantage. The division of aperture technique,for example, consists of an array of mini-cameras each with
its own spectral filter. For an array of 25 cameras [as shownin Fig. 2(a)], the system pupil is 25 times as large as the pupil
Optical Engineeringof each individual camera. Thus, if we compare a fullthroughput technique with a DoAp, we can say that the simplicity of the DoAp should allow one to implement a larger
pupil than the snapshot technique can, and this should
improve light collection. A similar argument holds for themultispectral filter array camera: using focal plane division
techniques allows one to use front end optics with lower
resolution than a comparable snapshot system, and this resolution change can be achieved simply by increasing the pupil
diameter, which improves on light collection.* In practice,
however, the tradeoff between complexity and light collection has not significantly impacted instruments presented
within the journal literature: the DoAp and DoFP approaches
so far constructed (see Refs. 14, 16, and 19) do not show anorder of magnitude larger pupil diameters than their fullthroughput counterparts have been able to achieve (seeRef. 27).
Note that although CASSI, IRIS, and MSI all suffer from
a 50% efficiency loss (the first due to the use of a binarymask, the others due to the need to polarize incoming
light), these are still labeled as “full-throughput” techniques
because the factor of two in light lost will be much lower
than the factor of N advantage due to snapshot collection.
CTIS also suffers from significant light loss due to inefficiencies in grating dispersion into the designed diffractive orders,
but this factor will also generally be small in comparison to
N. Finally, while one advantage of snapshot instruments isthe absence of scanning artifacts when imaging moving
objects, this does not imply that one obtains the full data
in real time. Both CTIS and CASSI are computationallyintensive instruments, and this can create a considerable
delay between raw data acquisition and the final delivery*Since cameras are more often than not operated in the aberration-limited
regime rather than diffraction-limited, increasing the pupil size results inincreased aberrations and loss of resolution.

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November 2012/Vol. 51(11)Hagen et al.: Snapshot advantage: a review of the improvement in light collection for parallel high-dimensional measurement systemsof the datacube. An overview of the various snapshot instruments and their maximum theoretical efficiency values are
given in Table 1.
4 Snapshot High-D Systems
The snapshot advantage in imaging spectrometry is a direct
analogue of the advantage of staring versus scanning infrared
imagers demonstrated during the 1980s and 1990s.44–47
Scanning infrared imaging systems used single-point detectors scanned in two dimensions across a scene, or a linear
array of detector elements scanned across one dimensionof the scene, in order to obtain a complete 2D image. Scanning systems suffered an efficiency loss equal to the numberof elements in the scan dimension as a direct result of using
a lower-dimensional detector array (single detector or 1D
array) to measure a higher-dimensional dataset, the 2D
image. This is equivalent to the imaging spectrometer problem of detecting a 3D dataset on a lower-dimensional
2D detector array. While infrared detectors evolved toallow detectors whose dimensionality matched the measurement data (2D for an image), the only way for an imaging
spectrometer to avoid scanning is to design an optical system
in which the light distribution on the 2D detector arrayencodes the full three-dimensional distribution of lightwithin the object’s datacube. Doing this encoding without
sacrificing light achieves the snapshot advantage.
The concept of a snapshot advantage also extends beyond
just imaging spectrometry. It applies equally well to any
high-dimensional (high-D) system—an instrument whose
data dimensionality is higher than just the two dimensions
available for detector arrays. The plenoptic function
Iðx; y; z; θx ; θy ; λ; s; tÞ describes the complete distribution ofdata obtainable from passively sampling the optical field,48
and thus describes the highest data dimensionality to which
we have ready access via optics. (Here s and t describe thepolarization and time variation of the optical field.†) Since
higher-dimensional measurement systems parcel the finite
number of photons collected into ever smaller bins, maintaining snapshot capability becomes important for anything
beyond the measurement of static objects in a laboratory
setting.
The “light field camera,” for example, is a snapshot
instrument which collects angularly resolved image data
Iðx; y; θx ; θy Þ by re-mapping the 4D distribution onto a
two-dimensional detector array.49 A similar but much lesscompact implementation uses an array of individual cameras.50 These snapshot aprroaches thus have a N θx × N θythroughput advantage over any system which scans overangle in order to obtain the full dataset.‡ This is separate
from the reduced signal-to-noise ratio in each data element
due to the use of smaller bins that come with higher
dimensionality measurement. Snapshot techniques thus
become increasingly important with increasing dimensional†

Since s is restricted to a discrete space of only a few elements (with the exact
number of elements depending on one’s choice of polarization representation) it is arguably not a “dimension,” or, at least, not a dimension of thesame nature of the remaining seven elements of the plenoptic function.

‡

The size of the dataset delivered by this instrument illustrates some of thecomplexity tradeoff for full-throughput snapshot measurement. By samplingin angle over a ðN θx ; N θy Þ ¼ ð14; 14Þ domain, the number of detector pixels
required increases by 142 ¼ 196. Obtaining megapixel spatial sampling in asnapshot is thus unobtainable with all but the largest mosaicked detector
arrays available today.

Optical Engineering

ity, with the tradeoff that much larger detector arrays areneeded to accommodate the larger datasets.
Other examples of snapshot high-D systems include channeled imaging polarimeters,51–53 which measure an Iðx; y; sÞdataset; line imaging spectropolarimeters54,55 which measureIðx; λ; sÞ; and computed tomographic imaging channeledspectropolarimeters56,57 (CTICS), which measure Iðx; y; λ; sÞ.
For polarization systems, the snapshot advantage in lightefficiency is limited, since the theoretical maximum efficiency improvement over a scanning system is only 4 (fora Stokes polarimeter) or 16 (for a Mueller matrix polarimeter). Since polarimetry typically requires computational
reconstruction of the data, the need for accurate calibration58
means that snapshot systems’ lack of moving parts is usually
the more important feature.
5 Conclusion
When measuring high-D data, full-throughput snapshot
instruments have a light collection capacity which exceedsthat of all scanning and all throughput-division snapshot
instruments by a simple geometric factor which we callthe snapshot advantage. Any experimental setup whose
measurement dimensionality exceeds that of the detector,
and in which all data elements (e.g., datacube voxels in imaging spectrometry) are luminous throughout the measurement period can use this advantage fully. While there
currently exist only a handful of instruments capable offull-throughput snapshot measurements of 3D or 4D data,
we expect to see more as researchers find new ways of adapting new technology to these challenging measurements.
Since the full-throughput snapshot techniques map eachelement in the data to an individual pixel, the primary limitation to constructing snapshot versions of such instruments is
the limited number of pixels available with current detector
arrays, such that any system attempting to perform snapshot
measurements beyond 4D will need to wait for the development of much larger detector arrays. At some point instrument designers may learn how to relax this “curse ofdimensionality”59 by taking advantage of ideas such as compressive sensing,60 but we have not yet learned to do thiswhile maintaining data fidelity.
Acknowledgments
This work was partially supported by National Institutes of
Health (NIH) Grants RO1-CA124319 and R21-EB009186.
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Nathan Hagen worked for Thermawave(now KLA Tencor) from 1996 to 2002, as amember of the R&D team developing opticalmetrology instruments. He graduated with a
PhD degree in optical sciences at the University of Arizona in 2007, studying snapshot
imaging spectrometry and spectropolarimetry (including CTIS and CTICS). From 2007
to 2009, he worked as a postdoc at Duke University, developing imaging and spectrometry techniques (including CASSI). He joined
Rice University as a research scientist in 2009, where he joined
the effort to develop the IMS imaging spectrometer, and to continue
developing new imaging and spectrometry techniques.
Robert Kester is the chief technology officer
and co-founder of Rebellion Photonics. He is
also a co-inventor of the image mapping
spectrometer (IMS) technology being commercialized by Rebellion Photonics andhas extensive experience designing, fabricating, and testing optical devices. He has 10+
years of optics related experience and currently has 8 peer-reviewed publications and2 pending patents. He has a MSc from theCollege of Optical Sciences, University of
Arizona, Tucson, AZ and a PhD in Bioengineering from Rice University, Houston, TX.
Liang Gao received his BS degree in physics
at Tsinghua University in 2005 and his PhD
degree in applied physics at Rice University
in 2011. He is currently a postdoctoral
research associate in bioengineering at Rice
University, Houston, Texas, in the laboratoryof Tomasz Tkaczyk. His research interests
include microscopy, optical design and fabrication, and biomedical imaging.

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November 2012/Vol. 51(11)Hagen et al.: Snapshot advantage: a review of the improvement in light collection for parallel high-dimensional measurement systems

Tomasz S. Tkaczyk is an assistant professor of bioengineering and electrical andcomputer engineering at Rice University,
Houston, Texas, where he develops modern
optical instrumentation for biological andmedical applications. His primary researchis in microscopy, including endoscopy, costeffective high-performance optics for diagnostics, and multidimensional snapshot
imaging systems. He received his MS and
PhD degrees from the Institute of Micro-

Optical Engineering

mechanics and Photonics, department of Mechatronics, Warsaw
University of Technology, Poland. Beginning in 2003, after his postdoctoral training, he worked as a research professor at the College of
Optical Sciences, University of Arizona. He joined Rice University inthe summer of 2007.

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