Optical Engineering 52(9), 090901 (September 2013)

REVIEW

Review of snapshot spectral imaging technologies
Nathan Hagen
Rebellion Photonics Inc.
7547 South Freeway
Houston, Texas 77021
E-mail: nhagen@optics.arizona.edu
Michael W. KudenovNorth Carolina State University
Department of Electrical & Computer Engineering
2410 Campus Shore Drive
Raleigh, North Carolina 27606

Abstract. Within the field of spectral imaging, the vast majority of instruments used are scanning devices. Recently, several snapshot spectral
imaging systems have become commercially available, providing new
functionality for users and opening up the field to a wide array of new applications. A comprehensive survey of the available snapshot technologies isprovided, and an attempt has been made to show how the new capabilities
of snapshot approaches can be fully utilized. © The Authors. Published by SPIE
under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of thiswork in whole or in part requires full attribution of the original publication, including its DOI. [DOI:
10.1117/1.OE.52.9.090901]

Subject terms: snapshot; imaging spectrometry; hyperspectral imaging; multispectral imaging; advantage; throughput; remote sensing; standoff detection.
Paper 130566V received Apr. 15, 2013; revised manuscript received Jul. 30, 2013;
accepted for publication Aug. 1, 2013; published online Sep. 23, 2013.

1 Introduction
Spectral imaging sensors sample the spectral irradianceIðx; y; λÞ of a scene and thus collect a three-dimensional(3-D) dataset typically called a datacube (see Fig. 1). Since
datacubes are of a higher dimensionality than the twodimensional (2-D) detector arrays currently available, systemdesigners must resort to either measuring time-sequential
2-D slices of the cube or simultaneously measuring all
elements of the datacube by dividing it into multiple 2-D
elements that can be recombined into a cube in postprocessing. These two techniques are described here as scanningand snapshot.
The use of imaging spectrometers was rare before
the arrival of 2-D CCD arrays in the 1980s, but steadily
grew as detector technology advanced. Over the following
30 years, better optical designs, improved electronics,
and advanced manufacturing have all contributed to
improving performance by over an order of magnitude
since that time. But the underlying optical technology has
not really changed. Modified forms of the classic CzernyTurner, Offner, and Michelson spectrometer layouts remain
standard. Snapshot spectral imagers, on the other hand,use optical designs that differ greatly from these standard
forms in order to provide a boost in light collection capacity
by up to three orders of magnitude. In the discussion
below, we provide what we believe is the first overview
of snapshot spectral imaging implementations. After providing background and definitions of terms, we present
a historical survey of the field and summarize each individual measurement technique. The variety of instruments
available can be a source of confusion, so we use ourdirect experience with a number of these technologies[computed tomography imaging spectrometer (CTIS),
coded aperture snapshot spectral imager (CASSI), multiaperture filtered camera (MAFC), image mapping spectrometry (IMS), snapshot hyperspectral imaging Fouriertransform (SHIFT) spectrometer, and multispectral Sagnac
interferometer (MSI)—each described in Sec. 4 below] toprovide comparisons among them, listing some of theiradvantages and disadvantages.

Optical Engineering

1.1 Definitions and Background
The field of spectral imaging is plagued with inconsistent useof terminology, beginning with the field’s name itself. One
often finds spectral imaging, imaging spectrometry (or imaging spectroscopy), hyperspectral imaging, and multispectral imaging used almost interchangeably. Some authors
make a distinction between systems with few versus many
spectral bands (spectral imaging versus imaging spectrometry), or with contiguous versus spaced spectral bands(hyperspectral versus multispectral imaging). In the discussion below, we use spectral imaging to refer simply to any
measurement attempting to obtain an Iðx; y; λÞ datacube of ascene, in which the spectral dimension is sampled by morethan three elements. In addition, we use the term snapshot asa synonym for nonscanning—i.e., systems in which theentire dataset is obtained during a single detector integration
period. Thus, while snapshot systems can often offer muchhigher light collection efficiency than equivalent scanning
instruments, snapshot by itself does not mean high throughput if the system architecture includes spatial and/or spectral
filters. When describing a scene as dynamic or static, rather
than specifying the rate of change in absolute units for eachcase, we simply mean to say that a dynamic scene is one thatshows significant spatial and/or spectral change during themeasurement period of the instrument, whether that period
is a microsecond or an hour. Since snapshot does not by itself
imply fast, a dynamic scene can blur the image obtainedusing either a snapshot or a scanning device, the difference
being that whereas motion induces blur in a snapshot system,in a scanning system, it induces artifacts. In principle, blurring and artifacts are on a similar footing, but in practice
one finds that artifacts prove more difficult to correct inpostprocessing.
When describing the various instrument architectures,“pixel” can be used to described an element of the 2-D detector array or a single spatial location in the datacube (i.e., avector describing the spectrum at that location). While someauthors have tried introducing “spaxel” (spatial element) to
describe the latter,1 this terminology has not caught on, so we
simply use “pixel” when describing a spatial location whose
spectrum is not of interest, and “point spectrum” when it is.

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snapshot imaging
spectrometerline-sspec canning
trome
ter
point-scanningspectrometer

wavelengthscanning(filteredcamera)

y

y

x

x
(a)

(b)

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

While many authors refer to the spectral elements of a datacube as bands, we use “channel” to refer to individual spectral elements and reserve the use of bands for broad spectral
regions [such as the visible band or the longwave IR (LWIR)
band]. It is useful to have a terminology for a single horizontal plane of the datacube (the image taken over a single spectral channel), so we refer to this as a “channel image”.
A single element of the datacube is referred to as a “voxel”(volume element). When describing the dimensions of thedatacube, we use N x , N y , and N w as the number of sample
elements along the ðx; yÞ spatial and λ spectral axes, respectively, so that the total number of datacube elements is given
by N x N y N w. We try to avoid describing the datacube in termsof resolution, since many authors use this to refer to the number of sampling elements, while others refer to it as the number of resolvable elements. At the Nyquist sampling rate,
these two differ by a factor of two, but if one always refers
to the number of samples, then the meaning is clear. One canalso note that it is problematic to talk about a single value forresolution when discussing computational sensors, since thenumber of resolvable elements for these systems varies withthe scene—some scenes are easier to resolve than others.
For time-resolved (video imaging) systems, the data
dimensions assume the form (N x , N y , N w , N t ), where N t
is the number of frames captured during a video sequence.
We refer to this dataset as a “hypercube”.
The amount of light collected by a given instrument is an
important quantity, so we often refer to a given sensor’s
throughput or efficiency. Whereas the former refers specifically to the AΩ product (or “étendue”), the latter is a ratio of
the sensor’s throughput with respect to a reference sensor
that can collect light from the entire datacube during thefull measurement period and that also has ideal quantum
efficiency. Whereas the ideal instrument for any given application always has an efficiency of 1, its throughput varies
with different applications.
Also, many authors make a distinction between spectrometer, spectrograph, and spectroscope, with distinctions varying among researchers. We make no distinction here andgenerally stick to using spectrometer, except where thisclashes with a given field’s nomenclature.
Optical Engineering

2 Historical Overview
As in so much of optics, one can trace the beginnings ofspectral imaging back into the nineteenth century, where
one finds the astronomer P. J. C. Janssen using a doubleslit monochromator to view the solar corona.2,3 The double-slit monochromator (at the time termed a spectroscope,or in this case a spectrohelioscope) was the only means ofobtaining narrow-band spectra, and an image was obtainedby spinning the device rapidly while viewing the exit slit
with the eye. By adjusting the relative position of the exit
slit with respect to the prism dispersion, one could thus
view the same scene at different wavelengths. Although
an important4 and clever setup, it was regarded by otherresearchers as clumsy.5 Some three decades later, Fabry
and Perot developed their interferometric filter, which forthe first time allowed astronomers to both view a fullscene over a narrow spectral band and tune the filter wavelength.6–8 The tunable filter thus represented an important
advance, giving scientists access to information that waspreviously difficult to obtain. This allowed them to build
ðx; y; λÞ representations of the object in view, albeit
laboriously.
An additional advantage of the Fabry–Perot interferometer was that it allowed a much higher light throughput
than the double-slit monochromator, enabling users to view
dimmer objects. This opened up a number of discoveries,
but, as a spectral imager, it still suffered from two problems
that simple cameras do not: motion artifacts and poor lightcollection efficiency. These two issues have plagued the field
ever since. In order to overcome these problems, astronomers
began looking for nonscanning instruments that could obtainthe full 3-D dataset in a single measurement period—snapshot spectral imagers. The first published example of a snapshot spectral imaging system was not far behind. Bowen
developed his image slicer9 by placing a series of tilted
mirrors to slice the image into thin strips and then translateeach strip to form a single long slit. Walraven later took thisconcept and created a design that was easier to manufacture,using only a thick glass plate (with a 45 deg angle cut into
one end) cemented to a wedge-cut prism.10 The resulting
device is shown in Fig. 2. Once a beam of light enters the090901-2

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Fig. 2 Various views of a Bowen-Walraven image slicer, illustrating how the glass plate and wedge-cut prism combine to slice the optical beam intoa long slit. Shapes shown in yellow indicate the light passing through the slicer; the beam reflecting within the top plate is not shown for clarity.
(Adapted from Fig. 1 of Ref. 16.)

glass plate, the beam reflects due to total internal reflection,
except in those regions where the plate meets the prismedge, where the beam transmits. The succession of partialreflections and partial transmissions transforms the input
beam into a long slit, which can then be used as the input
to a slit spectrometer. Over the next few decades after
Bowen’s initial invention, a number of astronomers adapted
this slicing technique to telescopes around the world,11–14 but
the method still provided only modest gains over existing
instrumentation. It was with the 3-D instrument on theWilliam Herschel Telescope that the image slicing techniqueprovided a large leap forward in performance, allowing fora snapshot measurement of a 16 × 16 × 2100 datacube(∼5.4 × 105 voxels).15 For the first time, precision manufacturing, large-format detector arrays, and computers had
advanced to the point that snapshot approaches could display
capabilities going well beyond their scanning counterparts.
During this development, in 1958 Kapany introduced theconcept of placing a coherent fiber bundle at the image plane
and then reformatting the fiber output into a long thin line
for easy adaptation to one or more slit spectrometers.17
But it appears not to have been implemented until 1980,
when such a device was developed for the Canada-FranceHawaii telescope (CFHT) on Mauna Kea.18 Adaptations byother astronomers soon followed.19,20
A third snapshot spectral imaging technique was developed by Courtes in 1960, in which a lenslet array is used
to create an array of demagnified pupils.21,22 These pupils
fill only a small portion of the available space at theimage, so with the proper geometry one can reimage themthrough a disperser to fill in the unused space with dispersed
spectra. This concept was adapted to the CFHT and data
began to be collected in 1987, producing datacubes with
N x × N y ¼ 271 spatial elements and up to N w ¼ 2200 spectral samples.23
These three techniques for snapshot spectral imaging—
image slicing, fiber reformatting, and lenslet-based pupil
array dispersion—are now widely described in astronomy
as integral field spectroscopy (IFS), so we label the threetechniques here as IFS-M, IFS-F, and IFS-L. The integral
spectroscopy nomenclature appears to originate from thedissertation work of Chabbal,24 but the first publication inwhich one can find it used in the title is Ref. 25.
Outside of astronomy, one finds similar uses of slit spectrometers and tunable filter cameras, but the vast majority ofuses did not require imaging. These include measurements
Optical Engineeringsuch as mapping the spectrum of atomic emission/absorption
lines, measuring the chemical composition of the atmosphere,26 and measuring the quantity of physical compounds.27 Outside of astronomy, the coupling of imaging
with spectrometry did not take hold until much later, withthe beginning of airborne remote sensing. Here spectral imaging was first used for agricultural assessment and management around 1966 (Refs. 28 and 29) and received a large
boost with the launch of the Landsat remote sensing satellite
in 1972.30 With the launch of Landsat also came the development of field-portable spectral imaging instruments needed
to calibrate Landsat’s measurements. As spectral imaging
became more widely used, researchers faced the sameobstacles of scanning artifacts and poor light throughput
as those faced by the astronomers, so that they too began
to explore new methods, leading to a variety of new instruments. As single-pixel detectors gave way to linear andthen 2-D detector arrays, system design options expanded,allowing for new approaches. The first of these new
approaches derived from the natural idea of using multiple
beamsplitters, in which the beam is split into independent
spectral channels, with each channel directed to an independent camera. While this was a common choice for imaging inthree spectral bands, especially for wideband measurements(such as visible plus near-IR), it did not take hold for morethan four spectral channels. Hindrances included the difficulty of making large beamsplitters of high-enough quality
and the limited ability to reduce the bulk and weight of theresulting system. With the increasing availability of thin-film
filters, another natural choice involved using an array offilters coupled to an array of lenses. This, too, did not progress far, perhaps because of the difficulty of making large
arrays of lenses with sufficient quality and correction forparallax effects. (Ref. 31 comments that the first good thinfilm filters became available in the late 1930s. So we can
expect that they did not become commercially available until
the 1940s or 1950s.)
With the realization of advanced computers, the optionof a computational sensing32 approach became feasible. The
first of these new approaches was a computational sensor
later named the CTIS. This device used a 2-D disperser toproject a spectrally dispersed scene directly onto a detector
array, allowing the spectral and spatial elements to multiplex.
(One can experience the exact same thing by donning oneof the many diffraction grating glasses that are given out
at baseball games and fireworks displays.) The resulting

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data on the detector array are equivalent to tomographic
projections of the datacube taken at multiple view angles,
so that tomographic reconstruction techniques can be used
to estimate the 3-D datacube from the set of 2-D projections.
A compressive sensing approach33 to snapshot spectral
imaging was also developed, promising to allow snapshot
measurement of datacubes with more voxels than there are
pixels on the detector array.34 As of this writing, there is stilla significant amount of research that needs to be done withthese computational techniques, as they have not yet shown
performance that can compete with their noncomputationalcounterparts.35,36
3 Scanning Imaging Spectrometer Architectures
In parallel with the development of snapshot methods, scanning techniques for spectral imaging also advanced. The
development of linear digital sensor arrays allowed researchers to collect light from a number of voxels simultaneously.
This involved imaging a linear spatial region through asequential set of spectral filters or, more commonly, by collecting light over a full set of spectral channels while imaging
one spatial location and then scanning in two dimensions
over the full field of view—a point scanning spectrometer.
However, unless used with very wide spectral channels(such as on the Landsat satellites), the poor light collectionof these devices often made it difficult to use these instruments outside the lab.
Once 2-D detector arrays became available in the 1980s,
these were rapidly adopted in imaging spectrometers, providing a large boost in light collection capacity.37 For the firsttime, researchers had available systems that could collect
light emitted by thousands (and eventually millions) of voxels simultaneously. As array detectors advanced in size andperformance, instrument designers took advantage of the
new capability by increasing spatial and spectral resolution.
Using a configuration in which the 2-D detector arrayis mapped to a spectral plus one-dimensional spatial ðx; λÞdataset—a pushbroom spectrometer—made possible thefirst imaging spectrometers without moving or electricallytuned parts. If the sensor is placed on a steady-moving
platform such as a high-flying aircraft, an Earth-observing
satellite, or the object moves on a constant-motion conveyor,
the second spatial dimension of the cube is obtained simply
by scene motion across the instrument’s entrance slit. The
removal of moving parts greatly improved the robustnessof these devices and reduced their overall size, allowing
for image spectrometry to develop into a mainstream technology for Earth-observing remote sensing. Other architectures are also available for scanning systems, as summarized
below. A good review of these architectures and their relative SNRs is Ref. 38. Other surveys of scanning-based
approaches include Refs. 39, 40, and 41. (Note that Ref. 40’s
snapshot is equivalent to what we refer to here as a wavelength-scanned system or filtered camera.)
3.1 Point Scanning Spectrometer
The input spectrum is dispersed across a line of detector
elements, allowing for very fast readout rates. The scene
is scanned across the instrument’s input aperture with theuse of two galvo mirrors (or just one if the instrument
platform is itself moving), allowing for collection of a full3-D datacube.
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3.2 Pushbroom Spectrometer
The input aperture is a long slit whose image is dispersed
across a 2-D detector array, so that all points along a linein the scene are sampled simultaneously. To fill out the spatial dimension orthogonal to the slit, the scene is scanned
across the entrance aperture. This can take the form ofobjects moving along a conveyor belt, the ground moving
underneath an airborne or spaceborne platform, or the scene
scanned across the entrance slit by a galvo mirror.
3.3 Tunable Filter Camera
A tunable filter camera uses an adjustable filter (such asa filter wheel) or an electrically tunable filter, such as amechanically tuned Fabry–Perot etalon,42,43 a liquid-crystal
tunable filter (LCTF),44 and an acousto-optic tunable filter(AOTF).45 Response/switching times of the various
approaches range from ∼1 s for the filter wheel, to 50
to 500 ms for the LCTF and mechanically tuned Fabry–
Perot, and to 10 to 50 μs for the AOTF.
3.4 Imaging Fourier Transform Spectrometer
An imaging Fourier transform spectrometer scans one mirrorof a Michelson interferometer in order to obtain measurements at multiple optical path difference (OPD) values—
the Fourier domain equivalent of a tunable filter camera.46,47
A more recent alternative method here is the birefringent
Fourier-transform imaging spectrometer developed by
Harvey and Fletcher-Holmes, which has the advantage
of being less vibration sensitive due to its common pathlayout.48
3.5 Computed Tomography Hyperspectral Imaging
Spectrometer
This is a scanning device closely related to the CTIS snapshot technique mentioned above and has the advantage of
having a conventional disperser design and of being able
to collect many more projection angles so that the reconstructed datacube has fewer artifacts. Its main disadvantage
is that the detector is not used efficiently in comparison toalternative methods.49
3.6 Coded Aperture Line-Imaging Spectrometer
Although coded aperture spectrometry began as a methodof scanning a coded aperture across the entrance slit of aconventional dispersive spectrometer, in Refs. 50 and 51 it
was adapted to modern 2-D detector arrays, allowing for
improved SNR at the cost of using larger pixel count detector
arrays.
Each of these architectures uses passive measurement
methods, in which no control is required over the illumination in order to resolve the incident light spectrum. Several ofthese techniques can be used in reverse to produce spectrally
encoded illumination systems. In this approach, the object isilluminated with a well-defined spectral pattern, such that theimaging side no longer needs to have spectral resolution
capability. For example, one can illuminate a scene with abroadband light source transmitted through a tunable filter
and time the image acquisition to coincide with steps in
the filter wavelength to produce a datacube of light emitted
or reflected by the scene.

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Finally, when comparing scanning and snapshot devices,
we can note that the division between the two is not as black
and white as one might expect. For example, designers haveproduced sensor architectures that mix both snapshot andscanning techniques, so that the number of scans required
to gather a complete dataset is significantly reduced. The earliest example of this of which we are aware (although it
seems likely that astronomers had tried this well before
this time), is a patent by Busch,52 where the author illustrates
a method for coupling multiple optical fibers such that eachfiber is mapped to its own entrance slit within a dispersive
spectrometer’s field of view. More recently, we can findexamples such as Chakrabarti et al., who describe a grating
spectrometer in which the entrance slit is actually four separate slits simultaneously imaged by the system.53 The
respective slits are spaced apart such that the dispersed spectra do not overlap at the image plane. This setup can be used
to improve light collection by a factor of four, at the expenseof either increasing the detector size or reducing the spectral
resolution by a factor of four. Ocean Optics’ SpectroCam isanother example of a mixed approach, in which a spinningfilter disk is combined with a pixel-level spectral filter array(more detail on the latter is given in Sec. 4.8) to improve thespeed of multispectral image acquisition.
In addition, the fact that a given instrument is snapshot does
not in itself imply that the device is fast. Scanning devices canhave very short measurement times, and snapshot devices canpotentially have very long ones. The essential difference is thatsnapshot devices collect data during a single detector integration period, and whether this is short or long depends on theapplication. For large-format snapshot spectral imagers in particular, the frame readout rate can also be rather long in comparison to the exposure time, so that a video sequence (orhypercube) can be time-aliased due to poor sampling if thetwo rates are not forced to be better matched.
4 Snapshot Spectral Imaging Technologies
Before attempting a comparison of existing methods for performing snapshot imaging spectrometry, we go through themenagerie of instrument architectures and attempt to summarize the basic measurement principles of each one in turn.
Previous surveys (such as Refs. 54 and 55) have focusedon instruments developed for astronomy, while we attempt
here to discuss all of the techniques of which we areaware. In order to describe the various instruments, there
is an inevitable flood of acronyms. A selection of theseare summarized in Table 1, together with the section discussing each, the figure illustrating a typical system layout, andthe first reference to the technique.
4.1 Integral Field Spectrometry with Faceted Mirrors(IFS-M, 1938)
In astronomy, the most common approaches to snapshot imaging spectrometry are the integral field techniques (basedon mirror arrays, fiber arrays, and lenslet arrays: IFS-M,
IFS-F, and IFS-L)—so called because each individual measurement of a datacube voxel results from integrating over a
region of the field (the object). IFS-M was the first snapshot
spectral imaging technology to emerge, beginning with
Bowen’s image slicer. As originally conceived, this device
was both difficult to manufacture (due to precision alignmentof an array of small mirrors) and offered only a modest gain
Optical Engineering

Table 1 Location of summaries discussing each technology.

NameSectionFigureDate

Reference

IFS-M

4.1

3

1938

9

IFS-F

4.2

4

1958

17

IFS-L

4.3

5

1960

21

MSBS

4.4

6

1978

56

CTIS

4.5

7

1991

57

MAFC

4.6

8

1994

58

TEI

4.7

9

2000

59

SRDA

4.8

10

2001

60

IRIS

4.9

11

2003

61

CASSI

4.10

12

2007

34

IMS

4.11

13

2009

62

SHIFT

4.12

14

2010

63

MSI

4.13

15

2010

64

of 5× over existing slit spectrometers. In 1972, Walravenfound a way to modify the design to use a prism-coupledplane parallel plate in place of the mirror array.10,16 This
made the device much easier to align and assemble, but it
was still not very widely used, partly because its use wasprimarily limited to slow beams with f-numbers >30.65
It was not until the “3-D” instrument was completed on
the CFH telescope that image-slicer-type IFS could point toresults that were difficult to obtain with existing instruments
but that were readily obtained with the 3-D: performing spectroscopy and mapping the spatial distributions of dim
extended objects (such as nebulae or distant galaxies).15
Figure 3 shows a view of the image slicer subsystem for
an IFS-M. The 3-D instrument design, however, had several
limitations: in order to keep the pupils separated from one
another, the image slicer’s facet tilts had to be large, thus
inducing some defocus at the ends of the facet.
Furthermore, it was difficult to optimize the volume toincrease the number of facets and therefore the number ofspatial elements in the datacube. In 1997, Content showedthat allowing the microfacets to have curvature greatly
reduces these constraints, allowing the designer to reduce
the facet tilts and to place the pupils closer together—anapproached he named “advanced imaging slicing.”66,67
While adding curvature eases system design constraints, it
substantially complicates manufacture of the slicing mirror,
and researchers began a period of investigating how to
improve manufacturing techniques.68
Because of its all-mirror approach, the IFS-M technique iswell suited to measurements in the IR. It was also known that
although scatter induced by manufacturing artifacts, and bydiffraction at facet edges, was a serious problem at visible
wavelengths, it was much less so in the near-IR and

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y

rra

la
pi

pu

mi

rro
rs

slicer mirror

y

optic

fol
d

rra

la
pi

pu

al ax

fol
d

mi

rro
rs

is

(a)

(b)

Fig. 3 The system layout (a) for an integral field spectroscopy with faceted mirrors (IFS-M), and closeup (b) of the slicer mirror. For clarity, the layout
only shows the chief rays corresponding to each mirror facet, and the spectrometer optics behind each pupil have been omitted. (These back-end
optics are located behind each pupil in the array and include a collimating lens, disperser, reimaging lens, and detector array. If the mirror facets are
given curvature, then the collimating lens is unnecessary.)

Fig. 4 The system layout for an integral field spectrometer with coherent fiber bundles (IFS-F): the object is imaged onto the face of a coherent fiber
bundle. At the opposite end of the bundle, the fibers are splayed out (reformatted) into a linear array, which is compatible with the input of a standard
slit spectrometer. At the input and output faces of the fiber bundle, there may be lenslets coupled to each fiber in order to improve light throughput.

grating

lensletarray

objectobjective
lens

de

tec
arr torayintermediate
image

pupil
plane

Fig. 5 The system layout for an integral field spectrometer with lenslet arrays (IFS-L).

shortwave IR, and the image slicing method has been shown
to excel in these spectral bands.69 As confidence in manufacturing techniques increased, Content later introduced theconcept of microslicing (or IFS-μ), a technique that combines design elements of IFS-M with IFS-L. This enabled
one to measure many more spatial elements in the datacube,
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at the expense of reduced spectral sampling.70 The basic ideaof microslicing is to use the same slicing mirror as IFS-M,
but with larger facets. The slicer allows the various strips inthe image to be physically separated, and each is then passed
through an anamorphic relay, such that one axis is stretched.
This gives some extra space so that further down the optical

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path, the stretched image is relayed through an anamorphic
lens array, which simultaneously unstretches and samples theimage. The result is a format in which the various spatial
elements of the image take the form of narrow strips thatare sufficiently separated at the detector array that they canbe spectrally dispersed without adjacent strips overlapping.
The concept requires a mechanically elaborate design, but
promises to achieve an impressive datacube size of 1200 ×1200 × 600 or 1500 × 1500 × 200.70
4.2 Integral Field Spectrometry with Coherent Fiber
Bundles (IFS-F, 1958)
With the invention of coherent fiber bundles, it was quickly
realized that one can image through the circular bundle on
one end and squeeze the other end into a long thin line (creating what Kapany describes as a light funnel) to fit into thelong entrance slit of a dispersive spectrometer.17 It was quite
some time after this, however, that a working instrument was
deployed. Instead, one first finds examples in the literatureof systems that manipulate single fibers to positions within
the field of view—for example, placing one fiber at each ofa number of stars within the image.71 Rather than spectral
imaging per se, this is better termed multiobject spectroscopy. Allowing true spectral imaging through a fiber bundle
required first overcoming several hurdles, the first of which
was manufacturability. The process of reformatting the exit
face of the fiber bundle into a long slit generally produced a
lot of broken fibers, and replacing them is laborious. Anotherdrawback with the use of fibers was that it could be quitedifficult to couple light efficiently into them, so that a significant amount of light was lost at the incident face ofthe fiber. Moreover, if the cladding of the fibers is insufficiently thick, the fibers show significant crosstalk, whichquickly degrades the measurement quality. Finally, earlier
fiber-based systems were also restricted by the limited spectral range transmitted by available fibers. Improvements
in manufacturing and assembly techniques have steadily
reduced each of these problems. The use of multimode fibers
increased coupling efficiency,72 as did the use of lenslets registered to each fiber so that the light is focused onto the fibercores and not in regions with poor coupling efficiency. (Leeet al. mention that these fiber-coupling lenslets should be
used at f∕4 to f∕6.73) In addition, multimode fibers arealso more robust, so that it became easier to format theminto a line without breaking. With these and other advances,
fiber-based IFS systems were successfully deployed on telescopes.74 Figure 4 shows an example layout for an IFS-F
system.
A drawback with the fiber-based approach, it was learned,
was that the light emerging from the exit face of the fiber
was always faster (lower f-number) than it was on the
input face—a phenomenon that was termed focal ratio degradation.19,69,75 Another phenomenon that was discovered
when operating fiber-based systems at high spectral resolution was modal noise.76,77 In the midst of all of these developments, it was realized that the fiber-based approach also
allowed astronomers to do away with the free-space dispersive spectrometers that have been the mainstay of so muchof astronomical spectroscopy. If one can make use of components developed in the photonic industry, which has optimized miniaturization and manufacturing efficiency, then it
should be possible to minimize instrument size and cost in
Optical Engineeringmodern astronomical telescopes.78 Since photonic components are designed primarily for single-mode inputs, thisapproach first required the development of a device thatcan convert a single multimode input into a series of single-mode outputs—what has been called a photonic lantern.79 One of the great advantages of this integrated
photonic spectrograph approach80 is that it also enables
the ability to use high-precision optical Bragg filters to filter
out unwanted light from the atmosphere (often called OH
suppression).81
In parallel with the developments in astronomy, advancesin the technology also made it possible to build a commercial
spectral imager based on the same concepts. The firstnonastronomical instrument of which we are aware is thatof Matsuoka et al., which delivered datacubes of 10 × 10 ×
151 dimensions at 0.2 fps.82 This was followed by systems
developed by other research groups.83–87
4.3 Integral Field Spectroscopy with Lenslet Arrays(IFS-L, 1960)
The first discussion of using lenslet arrays for integral field
spectroscopy appears to be that of Courtes in 1960, in which
he proposes to use a lenslet array placed at the telescope’s
focal plane. Such a configuration generates an array of
pupil images—each mapped to a different field position.21,88(The first review of this concept in English appears to be
Meaburn’s in 1975, in what he calls an insect-eye Fabry–
Perot spectrograph.89) This is the basis of the lensletbased integral field approach. The lenslet array, placed near
the image plane, creates a series of pupil images—one foreach lenslet. Since the lenslets are at or near an image
plane, each pupil image comprises all of the light integrated
across the field positions corresponding to the spatial extent
of the lenslet. The advantage here is that one can allow thelenslets to create faster beams (with lower f-number) than theoriginal input, so that void space is created between the pupil
images. One can then take advantage of this space by dispersing the light across it, allowing for detection of the spectrum. Figure 5 shows an example layout for an IFS-L system.
The modern form of the IFS-L was first presented
by Courtes in 1980,22,23 but the first published data froman instrument did not follow until 1988, when Courtes
et al. present a system providing datacube dimensions of
44 × 35 × 580.90 As the concept spread, a number of otherastronomers began creating designs for different telescopes.73,91,92 Borrowing from terminology used in fiberbased integral field spectrometry, one difficulty with the lenslet approach is focal ratio degradation. The beam behind thelenslet array must have a smaller f-number than the beam infront of it, placing higher étendue requirements on the backend optics. One way of mitigating this issue is to use pinholes
in place of or in tandem with the lenslet array.93 The tradeoff
in doing this, of course, is that by spatial filtering one isreducing the system’s light throughput. In fact, if one replaces the lenslets with pinholes (so that one is sampling fieldpositions rather than integrating across them), then the lightthroughput of the system becomes no better than a scanningapproach.
While the IFS-L technique began in astronomy, its success brought it outside notice, and it was eventually adapted
to other spectral imaging applications, with the first publication demonstrating a system achieving datacube dimensions

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of 180 × 180 × 20, measured at 30 fps and f∕1.8 using a1280 × 1024 CCD.94,95
4.4 Multispectral Beamsplitting (MSBS, 1978)
The idea of using multiple beamsplitters for color imaging
has been around for quite some time.56 In this setup, threecemented beamsplitter cubes split incident light into threecolor bands, with each band observed by independent cameras [see Figs. 6(a) and 6(b)].96 While one can change thebeamsplitter designs to adjust the measured spectral bands,
it is not easy to divide the incident light into more than four
beams without compromising the system performance.
(Murakami et al., for example, limit themselves to four
beamsplitters and attempt to use filters to increase the number of spectral channels.97) Thus, four spectral channels
appear to be the practical limit of this approach. A closely
related method is to use thin-film filters instead of the bulkier
beamsplitter cubes/prisms to split the light,98 but thisapproach is still probably limited to about five or six spectral
channels due to space limitations and cumulative transmission losses through successive filters. The space limitation
can be overcome by using a single stack of tilted spectral
filters operating in double-pass, which allows for the entire
set of spectral images to be collected on a single detector
Rs

Fig. 7 The system layout for a computed tomography imaging spectrometer (CTIS).

array.99,100 (This is an approach we have previously termedfilter stack spectral decomposition.101) Although more compact than the previous methods, since the filters are now
operating in double-pass mode, transmission losses aredoubled as well, so this method is limited to N w < 6.
A fifth implementation is to perform spectral splittingwith a volume holographic element (VHE). Matchett et al.
have shown that they can manufacture a VHE to split an incident beam in three, with each of the three spectrally filteredbeams reflected at different angles.102 The VHE has the advantage of being a compact element with good reflectionensorchannel 5
sensorobjectivelens

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Fig. 6 System layouts for four different multispectral bemsplitter (MSBS) implementations, using (a) monolithic beamsplitter blocks, (b) a sequenceof spectral filters/beamsplitters, (c) a volume hologram optical element splitter, and (d) a stack of tilted spectral filters (or filter stack spectral
decomposition).

Optical Engineering

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efficiency over a reasonable range of field angles. But it
appears to be difficult to design the VHE for more than
three channels. For example, Matchett et al. divided the system pupil in four, using a different VHE for each of the four
sections, in order to produce a system that can measure 12
spectral channels. Matchett et al. state that this system hasachieved 60 to 75% throughput across the visible spectrum.
4.5 Computed Tomography Imaging Spectrometry(CTIS, 1991)
As with every other snapshot spectral imaging technology,
CTIS can be regarded as a generalization of a scanningapproach—in this case a slit spectrometer. If one opens
wide the slit of a standard slit spectrometer, spectral resolution suffers in that spatial and spectral variations across thewidth of the slit become mixed at the detector. However, if
instead of a linear disperser one uses a 2-D dispersion pattern, then the mixing of spatial and spectral data can be madeto vary at different positions on the detector. This allows
tomographic reconstruction techniques to be used to estimate
the datacube from its multiple projections at different view
angles. Figure 7 shows the CTIS system layout. The CTIS
concept was invented by Okamoto and Yamaguchi57 in 1991
and independently by Bulygin and Vishnyakov103 in 1991/
1992, and was soon further developed by Descour, who
also discovered CTIS’s missing cone problem.35,104,105 The
instrument was further developed by using a customdesigned kinoform disperser and for use in the IRbands.106 The first high-resolution CTIS, however, was
not available until 2001, providing a 203 × 203 × 55 datacube on a 2048 × 2048 CCD camera.107 Although the
CTIS layout is almost invariably shown using a transmissive
disperser, Johnson et al. successfully demonstrated a reflective design in 2005.108
A major advantage of the CTIS approach is that the systemlayout can be made quite compact, but a major disadvantage
has been the difficulty in manufacturing the kinoform dispersing elements. Moreover, since its inception, CTIS has had todeal with problems surrounding its computational complexity,
calibration difficulty, and measurement artifacts. These form acommon theme among many computational sensors, and the
gap they create between ideal measurement and field measurements forms the difference between a research instrument
and a commercializable one. While CTIS has shown a lotof progress on bridging this gap, it has not shown the ability
to achieve a performance level sufficient for widespread use.
4.6 Multiaperture Filtered Camera (MAFC, 1994)
An MAFC uses an array of imaging elements, such as an arrayof cameras or a monolithic lenslet array, with a different filter
placed at each element in order to collect portions of the full
spectral band (see Fig. 8). This first MAFC implementationof which we are aware is the Fourier transform spectrometer
approach by Hirai et al.58 Surprisingly, it was not until 2004
that we found an implementation like that shown in Fig. 8a,by Shogenji et al.,109 after which we find other researchgroups following the same approach.110,111 This layout uses
an array of lenses coregistered to an array of spectral filters,with the entire set coupled to a monolithic detector array.
(Note that the SHIFT system described in Sec. 4.12 describes
a similar, but filterless, Fourier-domain approach.)
Optical Engineering

Another approach was first suggested by Levoy113 andimplemented by Horstmeyer et al.114 This involves adapting
a light field camera with a pupil plane filter: a lenslet arrayis placed at the objective lens’ image plane, so that the detector
array lies at a pupil plane (as imaged by the lenslets). The
image behind each lenslet is an image of the filter array, modulated by the scene’s average spectral distribution across thelenslet. While more complex and less compact than the
Shogenji design, this second layout has the distinct advantage
of being able to use a variety of objective lenses, so that zooming, refocusing, and changing focal lengths are easier toachieve. Mitchell and Stone developed a similar techniquein which the linear variable filter is placed at the lenslet
plane.115
While the MAFC is arguably the most conceptually simple approach to multispectral imaging, it does place somerequirements on the scene’s light distribution in order towork well. For finite-conjugate imaging, it requires thatthe object irradiance is reasonably uniform in angle, sothat the individual filters and lenslets sample approximately
the same relative light distribution as do all of their counterparts. Specular objects are thus problematic at finite conjugates, and angular variations in irradiance will be mistakenly
measured as spectral variations.
4.7 Tunable Echelle Imager (TEI, 2000)
The tunable echelle imager (TEI) can be considered as amodification of an echelle spectrometer to allow imaging.
To make this possible, a Fabry-Perot etalon is placed into
the optical train so that the input spectrum is sampled by
the Fabry-Perot’s periodic transmission pattern.59,116 This produces gaps in the spatial pattern of the dispersed spectrum,
allowing one to fill the gaps with a 2-D image (see Fig. 9).
The light transmitted by the etalon is passed into a crossdisperser (for example, a grating whose dispersion is out ofthe plane of the page as shown in Fig. 9 and then into an
in-plane disperser). The result is a characteristic 2-D echelle
dispersion pattern, where the pattern is no longer composed ofcontinuous stripes, but rather a series of individual images,
each one of which is a monochromatic slice of the datacube(i.e., an image at an individual spectral channel). Underassumptions that the spectrum is smooth (i.e., bandlimited
to the sampling rate of the instrument), this achieves a snapshot measurement of the datacube. However, the main tradeoff
is that the system throughput is quite low: not only does theetalon reflect most of the input light, but the crossed-grating
format is also inefficient. Moreover, for cases in which theobject’s spectrum does not satisfy the bandlimit assumptions,the measurements are prone to severe aliasing unless scanning
is used to measure the gaps in the spectral data.
4.8 Spectrally Resolving Detector Arrays(SRDA, 2001)
With the development of Bayer filter array cameras in thelate 1970s, it became possible to produce single-pixellevel spectral filtering.117 The generalization from color imaging to multispectral imaging by increasing the number offilters is a small step (see Fig. 10), and there have been
numerous such proposals.60,97,118–126 The resulting instruments are extremely compact, since all of the spectral filtering is performed at the detection layer, but for several reasons
this method has not been widely accepted in the spectral

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lens arrayfilter
array

y

rra

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(a)

a
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(b)

lens arrayfilter arraylensletarray

object(c)filter
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image
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detector arrayobjective
lens

pupil
plane

Fig. 8 Layouts for a multiaperture filtered camera (MAFC) system, using (a) the Shogenji design, (b) IMEC112 design, or (c) the Levoy/Horstmeyer
design. (The color balls image is from http://commons.wikimedia.org/wiki/File:Toy_balls_with_different_Colors.jpg#.)

imaging community. The primary reasons are undoubtedlythat manufacturing these pixel-level filters is difficult andthat each pattern is highly specific, so that one cannot easilyadjust the system in order to change spectral range or resolution. The fact that the multispectral approach will generally
want to use detector arrays with higher pixel counts exacerbates the manufacturability problem. But another drawback
is that, as with any filtering technique, an increase in spectral
resolution produces a corresponding loss in light throughput.
Although Bayer-type filter-array approaches are compact,
convenient, and robust to perturbations such as temperaturechanges and vibration, they do have the disadvantage ofrequiring that the image is spatially bandlimited to the
Nyquist limit of the filter array (a limit that is typically several times stricter than the Nyquist limit of the underlying
pixel array). Without satisfying this assumption, the resulting
reconstructed spectral images may show substantial aliasing
effects, in which spatial variations in the scene will couple
into erroneous spectral variations in the measured datacube.
These effects can be minimized by defocusing the image inorder to satisfy the bandlimit constraint.
The spatial/spectral filter-based approach is one approach
toward adapting detector arrays to spectral resolving capability.
Optical Engineering

A number of other approaches are also under development,
which do not incorporate filters and thus have the potential
for an increased detection efficiency. Although developmenton spectrally resolved detector arrays with more than three
spectral bands has been underway for over 40 years,127,128
doing this for more than two spectral channels in snapshot
detection mode has only been pursued recently. The firststeps in this direction involved dual-band focal plane arrays[such as midwave IR (MWIR)/LWIR FPAs],129,130 but more
recently it has involved elements such as cavity-enhanced
multispectral photodetectors,131 elements composed of sandwiched electrodes and multiple detection layers,132 multilayer quantum-well infrared photodetectors (QWIPs),133
and transverse field detectors.134
The cavity-enhanced multispectral photodetector isdesigned by sandwiching several thin layers of amorphoussilicon (used as the detection layers) in a resonance-enhanced
cavity.135 Sun et al.131 and Wang et al.136 report on using thisapproach to measure two narrow spectral bands—one centered at 632 nm and another at 728 nm. Parrein et al. follow
a closely related approach in which the detection element
consists of layers of thin films sandwiched with multiple
transparent collection electrodes.132 This measurement

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10

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Fig. 9 The system layout for the tunable echelle imager (TEI). The box numbers in the raw data simulation shown here indicate wavelengths ofsubimages in nm; the dashed boxes indicate a replicate order of the Fabry-Perot etalon. (Figure adapted from Figs. 3 and 6 of Ref. 59.)

detection of absorbed photons within the detection layer.
Sensor electrodes spaced along the surface of the detector
array are biased to different voltages in order to generate thetransverse electric fields needed for each electrode to preferentially collect photocarriers produced at different depths.
While this trades off spatial resolution for depth resolution, it
provides a flexible method for depth-resolved detection.
In general, for multispectral detection (>3 spectral
channels), each of the filterless approaches are still underdevelopment, and thus considerable work remains before
they can be deployed for practical use.
4.9 Image-Replicating Imaging Spectrometer(IRIS, 2003)

Fig. 10 The system layout for a pixel-level filter array camera (oneimplementation of SRDA).

method combines the use of wavelength-dependent absorption depth with interference filters to create a stack of sensors
having strong wavelength-dependent signal collection. The
implementation of Ref. 132 so far allows only three spectral
channels to be resolved per pixel, but the approach shows
promise to allow resolution of more spectral channels.
Multilayer QWIPs are an alternative approach that has
seen considerable research.130 Mitra et al., for example,
present an IR detector consisting of a stack of multiple quantum well absorbers coupled through a diffractive resonantcavity.133 So far, this technique has been limited to three
spectral channels, though the concept is generalizable to
more.
Transverse field detection is a concept recently developed by Longoni et al.,134,137 allowing for depth-resolved
Optical Engineering

Lyot invented his tunable filter in 1938 based on the idea ofusing polarizers to turn the wavelength dependence of retardation in thick waveplates into a wavelength dependencein transmission.138 Although the instrument was refined byothers to use a different layout139 and to allow wider fields ofview,140,141 it could never measure more than one spectral
channel at once. In 2003, Harvey and Fletcher-Holmes
described a generalization of Lyot’s filter in which the polarizers are replaced with Wollaston beamsplitting polarizers.61
By splitting each incident beam in two, this technique allows
one to view a second spectral channel in parallel. By incorporating N Wollaston polarizers into the system, one canview 2N scenes simultaneously. The resulting layout, for a
setup using three Wollaston polarizers, is shown in Fig. 11.
The IRIS approach is an elegant solution that makes ahighly efficient use of the detector array pixels. So far,the IRIS approach has only been shown to operate withup to eight spectral bands,142 and it seems likely that difficulties of obtaining large-format Wollaston polarizers with
sufficient birefringence and that can correct for polarizationdependent chromatic aberrations may limit this approach
to about 16 spectral channels.143

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objectivelenscollimating
lens

re-imaging
lenspolarizer

objectwaveplates

Wollastonpolarizers

detectorarray

Fig. 11 The system layout for an image-replicating imaging spectrometer (IRIS). (The object simulated here is from http://en.wikipedia.org/wiki/
File:Colouring_pencils.jpg.)

4.10 Coded Aperture Snapshot Spectral Imager(CASSI, 2007)CASSI was the first spectral imager attempting to take advantage of compressive sensing theory for snapshot measurement.
Compressive sensing developed out of the work of EmmanuelCandes, Terence Tao, and David Donoho, typically involving
the use of L1 -norm reconstruction techniques to reconstruct
data that would be termed insufficiently sampled by the
Nyquist limit. The phrase is not intended to refer to a broad
category of reconstruction algorithms (such as computed
tomography) that can sometimes be said to permit compressive
measurement.
The concept for CASSI developed from a generalizationof coded aperture spectrometry.34 Coded aperture spectrometers replace the entrance slit of a dispersive spectrometerwith a much wider field stop, inside which is inserted abinary-coded mask (typically encoding an S-matrix patternor a row-doubled Hadamard matrix,144 see Fig. 12). Thismask attempts to create a transmission pattern at eachcolumn within the slit such that each column’s transmission code is orthogonal to that of every other column. This

Fig. 12 Top: the system layout for a coded aperture snapshot spectral imager (CASSI), showing only the single-disperser configuration.
Bottom: the pattern on the detector array due to imaging a coded aperture mask through a disperser, for an object that emits only three wavelengths (the wavelengths used in the example image here are theshortest, middle, and longest wavelengths detected by the system).

Optical Engineering

follows directly from the properties of Hadamard matricesthat each column of the matrix is orthogonal to every
other column. The encoded light, transmitted by the codedmask within the field stop, is then passed through a standard
spectrometer back-end (i.e., collimating lens, disperser,
reimaging lens, and detector array). Because the columns of
the coded mask are orthogonalizable, when they are smeared
together by the disperser and multiplexed on the detector
array, they can be demultiplexed during postprocessing.
The resulting setup allows the system to collect light overa wide aperture without sacrificing the spectral resolutionthat one would lose by opening wide the slit of a standard
slit spectrometer. The tradeoff is a factor of two in light loss
at the coded mask, and in some noise enhancement due tothe signal processing.
The theory of orthogonal codes only requires that the lightis uniformly distributed in one axis; the other axis can beused for imaging. This is analogous to a slit spectrometer,
which can image across its entrance slit. Using an anamorphic objective lens, one can achieve this by imaging theentrance pupil onto the field stop in one axis, while imaging
the object onto the field stop along the orthogonal axis.
Although one can consult references 145, 146, or 147 forfurther details on coded aperture spectral imaging, noneof these sources mention the requirements for anamorphic
front optics needed to achieve line-imaging with snapshot
coded aperture spectrometry.
Compressive sensing allows one to take a similar procedure and apply it to snapshot spectral imaging, measuring
ðx; y; λÞ in a snapshot and not just ðx; λÞ. The primarydifferences from the slit imaging case are that the aperture
code is no longer an orthogonal matrix but a random binary
matrix and that the reconstruction algorithm becomes much
more complex. The generalization proceeds as follows. If
one replaces the anamorphic objective lens with a standard
one, and images the object directly onto the coded aperturemask, then the irradiance projected onto the detector array
after passing through the disperser will be a mix of spatialand spectral elements of the datacube (see Fig. 12). The spatial-spectral projection at the detector array is modulatedby the binary mask in such a way that each wavelengthof the datacube experiences a shifted modulation code. If
this code satisfies the requirements of compressive sensing,then this is all one needs in order to use compressive sensing

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reconstruction algorithms to estimate the object datacube.34
The resulting system layout is not only extremely compact,
but also uses only a modest size detector array, so it iscapable of imaging at high frame rates. Wagadarikar et al.
showed the ability to capture 248 × 248 × 33 datacubes at
30 fps, though postprocessing of the raw data to produce
a hypercube (video datacube sequence) consumed many
hours of computer time.148 More recent algorithms are much
faster.36
Though compressive sensing holds out great promisefor future instrument development, designers have not yet
succeeded in creating an architecture that replicates its
basic requirements well. In rough form, one can summarize
the requirements as follows. The most basic feature isthat the measured object has to be compressible in somespace. For example, for an image represented in a wavelet
space, it is well known that one can almost always use
fewer coefficients than the number of pixels you wish toreconstruct in the pixel domain—this is a compressible
space for a typical image. If one were to measure the object
such that each measurement value was the projection of theobject onto a basis function in this compressive space, then
one would need far fewer measurements than if the systemmeasured all of a datacube’s voxels directly. Unfortunately,
one generally cannot design an optical system such that theobject can be measured in the compressive space directly(such as measuring an object’s wavelet coefficients).
Compressive sensing, however, provides an alternativethat is almost as good. Measurement vectors (we avoid calling them basis functions because they do not satisfy the general definition of a basis) that are composed of columns
within a random incoherent measurement matrix havebeen shown to replicate the properties of measuring in acompressive basis to very high probability. Using thistype of measurement matrix, however, comes with some
additional requirements. First, the measurement vectors
and the compressible basis functions must be mutually incoherent, which means that any element in one cannot be
expressed as a sparse linear combination of elements fromthe other.149 One can think of this in rough terms as having
measurement vectors highly spread out when expressed in
the basis vectors of the chosen compressible space, andvice versa. Also, the measurement vectors must satisfy isotropy, which means that they should have unit variance andare uncorrelated.150 Orthogonal matrices are one example ofsystems that satisfy this property.
Once a measurement is completed, the user applies areconstruction algorithm to estimate the object datacube.
The typical procedure for this is for the user to choose
the compressible basis in which to work (that is, onemust know a priori a basis in which the object is compressible) and apply an algorithm to estimate both the magnitudesof the coefficients and the set of measurement vectors comprising the space described by the product of the sensing andsignal compression matrices. The algorithm estimates thecoefficients and basis vectors by choosing an object representation that best approximates the actual measurement
while penalizing representations that have a larger numberof coefficients (i.e., are less sparse). For CASSI, a common
choice of basis has been total variation space in the x-y
dimensions (i.e., the object’s gradient image is assumed
to be highly compressible). While it is possible to adapt
Optical Engineering

the reconstruction algorithm to search for an optimal compressible basis (so that the user need not know this a priori),
this greatly burdens an already computationally intensive
problem.
The mathematics underlying this measurement approach
has seen a rapid advance in the last decade, but implementing
its requirements in hardware has been challenging. One of
the main obstacles is that, in order to obtain sufficient compression, the feature sizes used to create coded projections
are near the scale of the optical resolution. Not only does
this mean that characterizing the system measurement matrix
requires a great deal of care, but since the compressive sensing reconstruction methods are currently also sensitive toperturbations of the system matrix, the system is prone to
artifacts. Because of these issues, subsequent implementations of CASSI have used linear scanning, such that a 640 ×
480 × 53 datacube was reconstructed from a set of 24 frames(for a full collection time of about 2 s).151 In comparison withequivalent scanning instruments, this final result is disappointing, as even the authors admitted (see the concluding
remarks of Ref. 36), so it appears that considerable work
remains before we can take advantage of the compressive
sensing paradigm.
4.11 Image Mapping Spectrometry (IMS, 2009)
Image slicing, as accomplished by the IFS-M technique discussed in Sec. 4.1, is best suited for measurements with low
spatial and high spectral resolution. For many applications
such as microscopy, however, spatial sampling is the more
important quantity, and spectral sampling with only 10 to
40 elements is more common. This makes the IFS-M an
impractical approach in this field. While the microslicing
implementation (IFS-μ) is capable of achieving a muchhigher spatial sampling, this comes at the cost of a serious
increase in system design complexity. An alternative
approach is IMS. Like IFS-M, a microfaceted mirror isplaced at an image plane. Unlike image slicing, however,many of the mirror facets share the same tilt angle, sothat multiple slices of the image are mapped to each individual pupil. The resulting pattern, as seen by the detector array,resembles that of seeing a scene through a picket fence.
If there are nine individual pupils in the system, then thespaces between the fence’s slats are 1/9th the slat widths(see Fig. 13). One can see only thin slices of the scene,
but there are nine facet images on the detector array, each
representing the image shifted by 1/9th of a slat width relative to the others. Assembling all nine subimages thus
allows one to replicate the original scene. The advantageof obtaining these facet images is that one has separated
the elements of the scene enough so that there is space
to allow dispersion. By allowing each pupil to be shared
among many mirror facets, the system design becomes much
more compact and allows for higher spatial resolution.
The first IMS instrument (called an ISS at the time) provided a 100 × 100 × 25 datacube using a large-format CCD
array,62 but this was later improved to 350 × 350 × 46.152
As with image slicing (IFS-M), the primary drawback of
the IMS is the need for very high precision for cutting theimage mapper, which is the central element of the system.
Current ultraprecision lathes have advanced to the point
where it is possible to make these elements on monolithic
substrates, though considerable care is involved.

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objective lens

mapping
mirrorobject(a)(image of lorikeet)pplaupilnelen
arr sletaydeprarr ism
ay

tec

tor

arr

ay

(b)

(c)

(image without disperser)(image of uniform object)

Fig. 13 The image mapping spectrometer (IMS) system layout. Three different raw images are shown corresponding to a setup in which (a) the
lorikeet is being imaged through the full system (as shown), (b) the lorikeet is being imaged in a system in which the prism array has been removed,and (c) a spectrally and spatially uniform object is being imaged through the full system. (For clarity, in all three examples of raw detector data
shown here, the data are shown in color as if imaged by a color detector array, even though a monochromatic array is used in existing instruments.)(The lorikeet image is from http://commons.wikimedia.org/wiki/File:Rainbow_Lorikeet_MacMasters.jpg.)

4.12 Snapshot Hyperspectral Imaging Fourier
Transform Spectrometer (SHIFT, 2010)
The SHIFT spectrometer 63,153 performs its spectral measurement in the time domain and acquires image information
using a division of aperture approach. Conceptually, theidea is an extension of an earlier formulation—the multiple-image Fourier transform spectrometer (MIFTS) developed by Hirai in 1994.58 However, while the original
MIFTS was based on a Michelson interferometer and lensarray, the SHIFT spectrometer is based on a pair of birefringent Nomarski prisms behind a lenslet array. As depicted inFig. 14, an N × M lenslet array images a scene through two
linear polarizers surrounding a pair of Nomarski prisms.
Thus, N × M subimages are formed on a detector array.
Rotating the prisms by a small angle δ relative to the detector
array enables each one of the subimages to be exposed to adifferent OPD. Therefore, a 3-D interferogram cube can beassembled by sequentially extracting each one of the subimages. Fourier transformation, along the OPD axis of theinterferogram cube, enables reconstruction of the 3-D datacube. This prism-based design allows for a reduced system
volume and an improved robustness to vibration.
As with the original MIFTS system, the SHIFT can beconsidered as the Fourier transform analog of the MAFC,
and it offers many of the same advantages, such as compactness. Unlike the MAFC, however, it also offers continuously
sampled spectra and is more easily fabricated due to its use of
Optical Engineering

Fig. 14 The system layout for a snapshot hyperspectral imaging
Fourier transform spectrometer (SHIFT).

birefringent prisms. On the other hand, it also shares the
MAFC’s disadvantage of suffering from parallax effects.
4.13 Multispectral Sagnac Interferometer (MSI, 2010)
The MSI64 is an extension of channeled imaging polarimetry154 to imaging spectroscopy. The idea was conceptuallydemonstrated using the MSI depicted in Fig. 15. In this interferometer, incident light is divided by a beamsplitter into twocounter-propagating components. The component that was
initially reflected by the beamsplitter begins its propagation

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Fig. 15 The system layout for a multispectral Sagnac interferometer(MSI).

in the −z direction, where it gets diffracted away from theoptical axis by grating G2 . Reflection off of mirrors M2
and M1 guides the beam to grating G1 , where the beam isdiffracted in the opposite direction. The converse path istaken by the component that was initially transmitted by
the beamsplitter, thus allowing both beams to exit the interferometer collimated and dispersed laterally. The lateraldispersion induced by the gratings produces a lateral shear
S between the emerging wavefronts, where S is linearly dependent on the free-space wavelength λ. Additionally, gratings G1 and G2 are multiple order diffractive structures;i.e., the blaze contains deep grooves that impose morethan one wave of OPD. When these high-order sheared
beams converge through an objective lens and onto a detector array, a 2-D spatial interference pattern is generated. The
spatial frequency of this interference is directly proportional
to the diffraction order and, therefore, directly related to thegiven order’s spectral transmission.
These interference fringes are measured by the detector arrayas a superposition of coincident amplitude-modulated spatial
carrier frequencies. A 2-D Fourier transformation can be takenof the raw data to window and filter the amplitude-modulatedchannels in the frequency domain. Inverse Fourier transformation
yields the 2-D spatial data that correspond to the unique spectral
passbands generated by the gratings.
This system is essentially a multispectral approach inwhich many unique spectral slices are measured simultaneously on coincident interference fields. Its advantages
include inherent spatial coregistration between the bands
while offering simple postprocessing. However, its disadvantages lie in its implementation, namely, the spectral bands
must correspond to the grating’s orders. Additionally, only
one dimension in the Fourier space can be used to modulatespatial and spectral information. Therefore, more work must
be done to make this technique a viable competitor to any of
the other methods mentioned here.
5 Technology Comparisons
There are many ways to compare the various snapshot implementations, such as compactness, speed, manufacturability,ease of use, light efficiency, and cost. And while these are all
Optical Engineering

important, different system designers have different opinions
about each of these factors, so that any discussion canquickly devolve into an argument. In an attempt to avoid
explicitly taking sides, we have opted to compare the various
technologies on a more fundamental level—the efficiency
with which they make use of their detector elements.
Snapshot spectral imagers generally make use of large detector arrays and can push the limits of existing detector technology, so that their efficiency in using detectors correlates
closely with other important issues such as compactness,
speed, and cost. Allington-Smith1 has previously termed
this metric the specific information density Q: the productof the optical efficiency η (i.e., average optical transmission
times the detector quantum efficiency) with what can becalled the detector utilization ζ. The utilization is the numberof Nyquist-resolved elements R in the imaging spectrometerdatacube divided by the number of detection elements
M (pixels) required to Nyquist-sample those voxels. HereR ¼ Rx Ry Rw , where Rx , Ry , Rw denote the datacube resolution elements in the x, y, and λ directions. We modify thedefinition of ζ slightly from that of Allington-Smith sothat the numerator in ζ instead represents the number ofvoxel samples N required to achieve R. Thus, for a
Nyquist-sampled system, the two definitions for Q differ
by a factor of two in each dimension, whereas AllingtonSmith’s ideal value for Q is 1/8, and the ideal value
under our definition is Q ¼ 1. Letting Mu , Mv denote the2-D detector sampling elements, we have
Q¼η

NxNyNw
Mu Mv

for optical efficiency η. Allington-Smith also obtains specificformulas for Q for each instrument in terms of the systemdesign parameters, such as the aperture diameter and system
magnification. In order to show that the value for Q among
technologies stems from even more fundamental considerations than these, we assume ideal conditions for each
instrument type and derive the relevant efficiency from therequired margins at the focal plane needed to prevent significant crosstalk among elements of the datacube. Here crosstalk is defined as the condition where multiple voxels within
the measured datacube each collect a significant amount ofsignal from the same voxel in the true object datacube andwhere these two voxels are not physically adjacent to one
another in the datacube. For voxels satisfying this condition
but that are physically adjacent, we can call the effect blurrather than crosstalk.
For optical efficiency estimates η for each technology, we
assume ideal components, so that lenses, mirrors, prisms,
and gratings are assumed to have no losses (100% transmission or reflectivity), and that all detectors have an external
quantum efficiency of 1.
One of the reasons why we choose the detector utilization
ζ to define a metric for comparing technologies is that it is inmany ways a proxy for other important measures such as
manufacturability and system size. The connection arises
because, in various ways, all of the snapshot techniques
encode the spectral information by expanding the systemétendue. If all things are held constant except for the wavelength-dimension of the cube, then, in every instance,increasing N w requires increasing étendue. And this quickly
runs into difficult design constraints—for high-performance

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Nw
Nx
IRIS,
TEI,
MSBS,
MAFC,
SHIFT:IFS-L,IFS-F:

Ny

SRDA:

Nw

Ny

Nx

Nw

IFS-M,CASSI:IMS:

Ny

Fig. 16 Diagrams showing how the detector utilization formulas are calculated for each architecture, given the basic layout of how the datacube is
projected onto the two-dimensional detector array. Each square shown here represents a single pixel on the detector array. For clarity, eachsubfigure assumes N x ¼ N y ¼ 5, N w ¼ 16, and s ¼ 1. This value for the margin s is a practical minimum; working instruments use s ≥ 1 inorder to prevent serious problems with crosstalk. The MSI data are not shown here because of its complex layout.

systems one can only increase étendue by using larger andmore expensive optics (i.e., larger-diameter optical elementsthat can also handle a wide range of angles). Thus, snapshot
systems with lower ζ will generally reach this design ceilingbefore the higher ζ systems will, and either system size or the
angular acceptance of the optics must compensate for the difference in ζ.
The basic premise from which we derive the detector utilization ζ for each technology is that each technique requiresa margin around each subsection of the datacube, without
which blurring will cause significant crosstalk. For sometechnologies, smaller margins are easier to achieve thanfor others, but this factor is ignored here. Those technologies
that minimize the number of marginal pixels make the mostefficient use (have the highest utilization ζ) of a given detector array, but the actual value of ζ depends on the aspectratios of the datacube dimensions. For example, from
Fig. 16 we can see that the IFS-L and IFS-F technologies
use a similar format of projecting elements of the datacube
onto a 2-D detector array: each individual spectrum is dispersed, and because its neighbor spectrum is not necessarily
a neighboring spatial element, a margin must be used aroundeach spectrum to minimize crosstalk. If each spectrum isallowed a margin s pixels, then the number of detector pixels
M needed to capture an (N x , N y , N w ) datacube can be determined by the following calculation. For each individual
spectrum in an IFS-L or IFS-F, Fig. 16 shows that weneed N w pixels for the spectrum itself, 2N w pixels for the
top and bottom margins around each spectrum, and 6 pixels
for the margins on the two ends. Doing the same calculation
for s > 1, we see that each spectrum uses a rectangle on
the detector array with dimensions ðN w þ sÞ × ð2s þ 1Þ.
Multiplying this by the total number of spectra in the datacube, N x N y , we have
MIFS-F ¼ N x N y ðN w þ sÞð2s þ 1Þ:The value for ζ ≡ N∕M follows directly from this equation as
Optical Engineeringζ IFS-F ¼

NxNyNw
Nw¼:
N x N y ðN w þ sÞð2s þ 1Þ ðN w þ sÞð2s þ 1ÞIf the system architecture requires two pixels to measureeach voxel in the datacube, then the utilization is ζ ¼ 0.5.
For the IFS-M, IFS-μ, and IMS technologies, an N y × N w
swath is measured in a contiguous region on the detector
array, so that each swath requires a rectangular space ofðN w þ 2sÞðN y þ 2sÞ. Multiplying by the total number of
x-resolution elements in the datacube gives
M IFS-M ¼ N x ðN y þ 2sÞðN w þ 2sÞ:For the IRIS, TEI, MSBS, and MAFC technologies, eachsingle-channel slice of the datacube is measured as a contiguous region, so that each wavelength requires a rectangularspace of ðN x þ 2sÞðN y þ 2sÞ, and the total number of pixels
needed is
M IRIS ¼ ðN x þ 2sÞðN y þ 2sÞN w :For the filter-array implementation of SRDA, each pixel
samples an individual voxel, so that the utilization isinherently equal to 1. In the case of CASSI, we find that
M CASSI ¼ ðN x þ N w − 1ÞN y < N—that is, the utilizationis >1. In fact, the greater the number of wavelengths inthe datacube, the greater the utilization for CASSI. Note
that, due to problems achieving the micron-scale imaging
required to map code elements 1∶1 to detector pixel elements, existing CASSI instruments map code elements
1∶2, so that they use about four times as many detector pixels
ðpracticalÞ
as the theoretical value given here, i.e., M CASSI ¼
4ðN x þ N w − 1ÞN y .
There are two architectures used for CASSI: a single-disperser design (CASSI-SD) and a dual-disperser configuration (CASSI-DD). Ref. 155, in describing the CASSI-DD
measurement principle, contains errors implying that

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Table 2 The classification type of each technology, and ideal values
for the optical efficiency η and number of detector pixels used
(M ¼ Nζ) for each snapshot technology.

Class

η

M (pixels used)

IFS-F

F

1

N x N y ðN w þ sÞð2s þ 1Þ

IFS-L

F

1

N x N y ðN w þ sÞð2s þ 1Þ

IFS-M

F

1

N x ðN y þ 2sÞðN w þ 2sÞ

IFS-μ

F

1

N x ðN y þ 2sÞðN w þ 2sÞ

IMS

F

1

N x ðN y þ 2sÞðN w þ 2sÞ

IRIS

A

1∕2

ðN x þ 2sÞðN y þ 2sÞN w

MAFC

P

1

ðN x þ 2sÞðN y þ 2sÞN w

MSBS

A

1

ðN x þ 2sÞðN y þ 2sÞN w

MSI

F

1∕4

N x N y ð2N w þ 1Þ

SHIFT

P

1∕4

ðN x þ 2sÞðN y þ 2sÞN w

SRDA

F

1

Nx Ny Nw

TEI

AþF

1∕N w

ðN x þ 2sÞðN y þ 2sÞN w

CTIS

A

1∕3

∼N

CASSI

X

1∕2

N y ðN x þ N w − 1ÞTechnology

Note: Classifications: division of amplitude (A), division of field (F ),division of pupil (P), randomly encoded (X ), and computational
sensor (½ ).

CASSI-DD is even more compressive than CASSI-SD, sothat M CASSI−DD ¼ N x N y , achieving a detector utilization
equal to N w . The error can be found by a careful look at
Fig. 1 in Ref. 151, as well as in the mathematical descriptionof Sec. 2 there. Whereas the authors indicate that the form of
the data at the detector array is a cube, the architecture showsthat it must in fact be a skewed cube (an “oblique cuboid”).
This error also implies that the results reported in the paper
are in fact corrupted with spatial misregistration errors.
Table 2 summarizes the η and M values used to calculate
Q for each technology. In the table, note that for the computational sensors (CTIS and CASSI), the number of datacube voxels is related to the number of resolution elements N
not through the Nyquist sampling limit but through more
complex criteria. When calibrating these computational sensors, M is technically an arbitrary value, but in practice one
finds little value in allowing M to exceed the values shown in
the table. In addition, for the SRDA row in Table 2, it isassumed that the implementation uses the filter-array camera.
From Table 2 we can see that the MAFC/MSBS technologies
offer the highest Q for high spatial/low spectral resolution
datacubes (squat-shaped cubes), whereas the IFS-M/IFS-μ/
IMS options offer the highest Q for low spatial/high spectral
resolution datacubes (tall cubes). The latter do especiallywell when the spatial dimensions of the datacube are rectangular N x ≠ N y. As indicated in Table 2, the IRIS approach
Optical Engineering

behaves exactly as the MAFC/MSBS technologies, but loses
a factor of two due to its need to work with polarized input.
The IFS-L/IFS-F approaches suffer 3× loss in Q relative tothe mirror-based IFS technologies due to the extra factor of(2s þ 1) shown in the formula for M given in Table 2, arisingfrom the need to separate all spatial elements from one
another to avoid crosstalk.
Each of the technologies listed in Table 2 is also classified
according to the method used to divide the light into voxel
elements. The majority of technologies use division of field[F] (also called division of focal plane), in which the light iseither filtered or divided into separate beams according to its
placement within the image. Division of amplitude [A] is thenext most common method in which the light is divided into
separate beams by allocating a portion of light into eachbeam, as a simple cube beamsplitter does. Only two othermethods exist: division of pupil [P] (also called divisionof aperture) and compressive sensing [X].
5.1 Comments on Instrument Throughput
Fellgett156 and Jacquinot157 were the first researchers tocompare light collection efficiency for various spectrometer
technologies and to lead to categorizing what are now
commonly referred to as the Fellgett (multiplex) advantage
and the Jacquinot (throughput) advantage, both of which
are widely associated with Fourier transform and FabryPerot spectroscopy.158 More recently, researchers have argued
that with the advance of detectors to 2-D array formats andwith the majority of optical detector arrays used, from theultraviolet to MWIR, now being shot-noise-limited, both ofthese advantages no longer provide the improvement in
SNR that they once did.159 Sellar and Boreman, on theother hand, argue that while this appears to be true for the
Fellgett advantage, imaging Fourier transform spectrometers(imaging FTS, or IFTS) retain the Jacquinot advantage notbecause of their higher étendue but because they are able
to maintain a longer dwell time on each datacube voxel
than alternative technologies can.38 The authors also provide
a convincing case that the Jacquinot advantage can be considered as freedom from the requirement of having an entrance
slit, while the Fellgett advantage can be considered as freedom
from the requirement of having an exit slit. For filterless snapshot imaging spectrometers, both of the traditional advantages
are automatically satisfied: no exit slit is used (Fellgett), andthe instrument dwell time on every voxel is equal to the fullmeasurement period (Jacquinot).
It is useful to note that FTS approaches to scanning andsnapshot spectral measurement suffer from sampling efficiency losses at low spectral resolution, since a substantial
portion of the reconstructed spectrum (located at very low
wavenumbers) will lie outside the system’s true spectral
response range and so must be discarded. In detectornoise-limited applications, this effect is mitigated by thefact that while a fixed percentage of these samples do notcontribute to actual spectral samples after Fourier transformation, they do contribute to improving SNR in the measured spectrum.160,161 Spatial heterodyne interferometry
can be used to overcome the FTS’ sampling limitation at
low spectral resolution.162–165
In a previous publication, we have tried to steer thethroughput comparison argument away from its historicalfocus on étendue101 since the complexity of modern snapshot

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instruments makes any fundamental limits on étendue difficult to determine. Moreover, it has also been argued that, forscanning instruments at least, the differences in étendue
among different technologies is not large.38 Rather, we try
to focus on a more important factor—the portion of datacube voxels that are continuously visible to the instrument.
For scanning systems, this portion can be quite low (often<0.01), while filterless snapshot systems can achieve avalue of 1 (i.e., all voxels are continuously sensed during
the measurement period). This creates a large differencein light collection—a difference we have termed the snapshot
advantage. While a snapshot instrument’s absence of motion
artifacts and ability to work without moving parts are both
important, the snapshot advantage in light collection is thedifference from scanning systems that holds the most promise for opening up new applications.
While not all snapshot implementations can be consideredequal, Table 2 indicates that all but one technology (TEI)
share optical efficiency values within a factor of four of
one another. For most of the technologies summarized in
the table, the efficiency values shown are straightforward
to obtain and are generally not subject to major disagreement. Perhaps surprisingly, MAFC is the exception. As
the argument leading to our choice of η ¼ 1 for MAFC
requires a lengthy discussion, it has been moved to the
Appendix.
5.2 Using Snapshot Instruments in Scanning
Applications
Pushbroom-configuration spectral imagers have long beenused on moving platforms in remote sensing because theirview geometry is well suited to the system measurement
geometry: linear motion along one axis provides the neededscanning to fill out the third dimension of the data, so that nomoving parts are required in the system. Up until now, snapshot spectral imaging systems have been absent from environmental remote sensing, though computational speeds anddata transmission rates have reached a level at which one can

now fully utilize the snapshot advantage in light collection to
improve SNR. Because these types of measurements takeplace from a moving platform, achieving the snapshot advantage requires performing what one can call video-rate software time delay integration (TDI). That is, with eachacquired frame, the system must coregister and add the
new datacube with the previous set in order to build alarge high-SNR single datacube from the entire sequenceof data. Figure 17 shows how this works. Unlike with hardware TDI,166–169 where the data are not actually digitized
until they have been fully summed, software TDI performs
the summing after digitization and so is more prone to detector and digitization noise. In the regime of shot-noise-limited
data, however, these effects are small. While it is possible, in
principle, to design specialized detector arrays that would becapable of performing hardware TDI for a given snapshot
imaging spectrometer, these arrays would be highly specialized and thus expensive and difficult to obtain.
As an illustration, a snapshot system capable of collecting
a 200 × 500 × 200 datacube at standard frame rates (on theorder of 100 fps) can use software TDI to dwell on a given
spatial region for 200 times longer than an equivalentpﬃﬃﬃﬃﬃﬃﬃpushbﬃ
room spectrometer can, allowing for a factor of 200 ¼ 14
improvement in SNR for shot-noise-limited data. Recent
advances in data transmission formats (such as multilane
CoaXPress, Camera Link HS, and SNAP12 fiber optics)
have shown that the transmission rates required by sucha setup are now achievable in commercially available
hardware. Moreover, because of the parallel nature of thesoftware TDI operation on datacubes, recent GPUs canprocess this data stream at high-enough rates to keep up.
Together, these developments make the full snapshot advantage realizable even for moving platforms that are nominallyoptimized for pushbroom operation.
5.3 Disadvantages of Snapshot
Snapshot approaches are not without their tradeoffs. The
system design is generally more complex than for scanning

Fig. 17 A diagram showing the two types of time-domain integration (TDI): (a) hardware TDI and (b) software TDI. In conventional (hardware) TDI,
the pixel data are shuttled across the detector at the same rate as the image motion. The sequence shown here consists of five frames in which theimage is moving diagonally across the array. In (b), the same basic concept is employed, but instead of shuttling charges across the array, thedatacubes are first digitized and then registered/added in postprocessing. (The lorikeet image is from http://commons.wikimedia.org/wiki/File:
Rainbow_Lorikeet_MacMasters.jpg.)

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systems and makes use of recent technology such aslarge FPAs, high-speed data transmission, advanced
manufacturing methods, and precision optics. Moreover,the snapshot advantage in light collection often can be
fully realized only by tailoring the design to its application.
For example, we have taken outdoor measurements with anðN x ; N y ; N w Þ ¼ ð490;320; 32Þ snapshot imaging spectrometer that reads out at 7 fps, but used an exposure time of
only 6 ms to avoid saturation. This exposure time is poorly
matched to the readout rate, so that most of the snapshot system’s light collection advantage is thrown away. An application for which these are much better matched would
require a much dimmer scene or a much faster readout rate.
It is also important to recognize that there are measurement configurations for which snapshot spectral imaging
is actually impossible to realize. Confocal microscopy is aclear example. Here the light is confined by a small aperturein order to reject light emerging from unwanted regions of
the sample (i.e., outside the focal volume).170 Thus, thismethod for rejecting unwanted light means that only one
spatial point is in view at any given time, and one mustscan the optics about the sample in raster fashion in orderto generate a complete ðx; y; λÞ spectral image. By its nature
this prevents a snapshot implementation. On the other
hand, for the case of volumetric imaging microscopy, there
exists an alternative technique—structured illumination
microscopy—that is compatible with widefield imaging, andthus with snapshot spectral imagers, and that in some cases
can achieve better SNR than can confocal microscopy.152,171
An additional difficulty with using snapshot systems isthe sheer volume of data that must be dealt with in orderto take full advantage of them. Only recently have commercial data transmission formats become fast enough to fully
utilize a large-format snapshot imaging spectrometer for daylight scenes. (Multi-lane CoaXPress is an example of such aformat.) There are ways of reducing the data glut. For moving platforms, performing software TDI prior to transmitting
the data allows high SNR data without requiring any bandwidth beyond those used by scanning systems. For target
detection and tracking systems, one can process filter detection algorithms onboard prior to transmitting the data, so thatrather than the full cube, one only needs to transmit thedetection algorithm result. For transmitting complete datacubes, one can also resort to onboard compression.172
6 Conclusions
Over the past 30 years, scanning techniques have seen an
impressive improvement in performance parameters, including calibration stability, SNR, and spatial, spectral, or temporal resolution. This trend can be attributed to larger
detector arrays, reduced detector noise, improved systemdesign, and better optical/optomechanical manufacturing;but the underlying technology and concepts have notchanged significantly in this time period.
The advent of large-format (4 megapixel) detector arrays,
some 20 years ago, brought with it the capability to measuremillions of voxels simultaneously, and it is this largescale measurement capacity that makes snapshot spectral
imaging practical and useful. Almost all research in snapshot
spectral imagers use novel 2-D multiplexing schemes, eachof which involve fundamental tradeoffs in detector pixel
utilization, optical throughput, etc. While many advantages
Optical Engineering

can be realized for these snapshot systems over their temporally scanned counterparts, it is only by making use of large
arrays of detector elements that these advantages can beachieved. And it is only in the past 10 years that the spatialand spectral resolution achieved by snapshot imaging systems has become sufficient that the devices are now commercially viable. We can anticipate that the snapshot advantage
will open up a number of new applications that leverage
the improvements in light collection, temporal resolution, or
ruggedness. The next 10 years should see further improvements in the technologies reviewed here with continued
advancements in detector array technology, optical fabrication, and computing power.

Appendix: Optical Efficiency of MAFC
Systems
In order to explain our choice of η ¼ 1 for MAFC’s efficiency factor, we attempt to provide an argument fromtwo sides and explain why we feel one perspective should
be given more weight.
One way to view the optical throughput is from a voxel’sview of the system. That is, we consider a voxel emitting
light as a Lambertian source and thus fully and uniformly
illuminating the instrument’s pupil. When comparing each
instrument, if we set the pupil area and system focal length(and thus the f-number) to be the same for all instruments,
then the efficiency is simply the fraction of light entering thepupil that reaches the detection layer. For the MAFC, lightemitted by the object voxel illuminates the system pupil, but
only one of the N w lenses in the MAFC objective lens arraycan transmit the voxel’s light to the detection layer. The
remaining N w − 1 lenses have to reject this voxel’s light,
so from the voxel perspective, the MAFC is effectively performing spatial filtering of the pupil, so that the transmitted
light flux is reduced by 1∕N w. And thus this perspective
argues for giving the MAFC an efficiency η ¼ 1∕N w.
A second way to view the optical efficiency is to see how
the system’s optical efficiency scales with a change in thenumber of wavelengths N w . For the MAFC, increasing
N w means increasing the number of lenses in the objective
lens array, and with them the number of filters as well. Whenscaling a lens array like this, if one momentarily ignores thefilters, it can be readily observed that the irradiance on thedetector is invariant to scale when viewing extended objects.
This contradicts the previous voxel view—a fact that can be
explained as follows.
When we increase the number of lenses in the array by ascale factor S2 (e.g., S ¼ 2 increases the number of lenses byfour), the lens focal lengths drop by the factor S. If the scaled,
smaller lenslets have the same f-number that the unscaled,larger lenslets had, then we should find that the irradianceat the focal plane (ignoring filters) is independent of the number of lenslets when imaging an extended object. But thiswould appear to conflict with the voxel view expressed
above. The feature that is easy to miss is that by scaling
the lenses we have changed the magnification, so that thevoxel we were imaging in the unscaled system is now
1∕S2 of a voxel in the scaled system. The scaled version
is effectively integrating across larger regions of the object.
One can also explain this as an increase in the étendue of thepupil. That is, after scaling the system, the maximum range

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of angles passed by the pupil (what may be called the pupil
acceptance angle) has increased by S in each axis. And this is
the difference between the two perspectives on how to measure the system’s efficiency: the pupil étendue of the scaled
system is S2 times that of the unscaled system, effectively
cancelling out the 1∕N w optical efficiency factor. Thus,
although increasing N w means that the spectral filters inthe system will transmit a smaller fraction of the incident
light, the shorter focal length lenses allow a higher étendue,
and the two effects cancel to give η ¼ 1.
At this point, neither of the two views can be described as
the correct view—they both simply describe different properties of the system. So we make use of some empiricalobservations. In general, one finds that MAFC systems
have a substantially larger system pupil (the pupil of eachindividual objective lens multiplied by the number of lenses
in the array) than do the objective lenses of other instruments
such as CTIS, IRIS, IMS, etc. Moreover, one can observethat the MAFC also has a larger acceptance angle of thepupil than do the other systems. However, if we compare
MAFC’s pupil étendue with, say, IMS’s étendue—measured
not at the IMS objective lens pupil but rather at the system
pupil of the IMS’s back-end lenslet array—then we obtaincomparable values. Thus, the limiting étendue of these systems is generally determined not by their monolithic frontoptics but rather by their optical arrays. Although thisstretches the definition of optical efficiency from a system
performance perspective, it is clear that we should choose
the system scaling view over the voxel view, so that MAFC’s
efficiency factor η is 1 and not 1∕N w .
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090901-22

Nathan Hagen graduated with a PhD degree
in optical sciences at the University of
Arizona in 2007, studying snapshot imaging
spectrometry and spectropolarimetry (including CTIS). From 2007 to 2009, he worked asa postdoc at Duke University, developing imaging and spectrometry techniques (including CASSI). From 2009 to 2011 he worked
as a research scientist at Rice University,
continuing work on imaging and spectrometry, including development work on the

September 2013/Vol. 52(9)Hagen and Kudenov: Review of snapshot spectral imaging technologies
IMS imaging spectrometer. In 2011 he joined the newly formed
Rebellion Photonics, to help develop snapshot imaging spectrometers as commercial products.
Michael W. Kudenov completed his BS
degree in electrical engineering at the
University of Alaska in 2005 and his PhD
in optical sciences at the University of
Arizona in 2009. He is currently an assistantprofessor in the Electrical and Computer
Engineering Department at North Carolina
State University. His research focuses on visible-light and thermal-infrared spectrometer,interferometer, and polarimeter systems
development and calibration. Applications
span disease detection, chemical identification, remote sensing, fluorescence imaging, polarimetry, spectroscopy, polarization ray tracing
and aberrations, and profilometry.

Optical Engineering

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September 2013/Vol. 52(9)