[Blue Header]

Coded Aperture Snapshot Spectral Imaging (CASSI)

Experimental CASSI data

We have recently constructed a new single disperser CASSI prototype. Links to papers describing the instrument, experimental data and the associated Matlab code to reconstruct a datacube from the data are provided here.

 

Spectral imaging is a technique that generates a spatial map of spectral variation, making it a useful tool in many applications including environmental remote sensing, military target discrimination, astrophysics and biomedical optics. When imaging a scene, a spectral imager produces a two-dimensional spatial array of vectors which represents the spectrum at each pixel location. The resulting three-dimensional dataset containing the two spatial dimensions and one spectral dimension is known as the datacube.

Many different techniques for spectral imaging have been developed over the years. Whiskbroom, pushbroom and tunable filter imagers are all conceptually simple spectral imager designs. These instruments capture a one- or two-dimensional subset of the datacube, and thus require the temporal scanning of the remaining dimension(s) to obtain the complete datacube. Furthermore, they have poor light collection efficiency for incoherent sources, resulting in a poor signal-to-noise ratio (SNR). Multiplex spectral imagers including Fourier and Hadamard transform based instruments are designed to address the light throughput problem, but still require some form of scanning, making it difficult to use them for spectral imaging of non-static scenes.

Tomographic approaches have also produced major advances. Mooney et al. developed a direct-view design that maximizes the light gathering efficiency by not requiring any spatial filter, such as a slit. With this design, the source is viewed through a rotating dispersive element. Measurements are taken at different rotation angles. These measurements are projective measurements through the datacube that can be tomographically reconstructed. While the light gathering efficiency of such an instrument is high, the geometry of the system limits the range of angles over which projections are made. As a result of the Fourier slice theorem, this results in an unsampled region in the Fourier space, a problem known as the ``missing cone problem'', because the unsampled region is a conical volume in the Fourier domain representation of the datacube. The computed tomography imaging spectrometer (CTIS) system is a static, snapshot instrument that captures multiple projections of the datacube at once. These capabilities make the CTIS instrument ideal for spectral imaging of transient scenes. However, the instrument requires a large focal plane area and also suffers from the missing cone problem.

The CASSI revolution

An important characteristic shared by all the designs described above is that the total number of measurements they generate is greater than or equal to the total number of elements in the reconstructed datacube. In contrast, our group has introduced the idea of compressive spectral imaging, an approach to spectral imaging that intentionally generates fewer measurements than elements in the reconstructed datacube. We utilize the power of compressed sensing ideas (to be described below) to solve our underdetermined problem by relying on a crucial property of natural scenes, namely that they tend to be sparse on some multiscale basis. To achieve compressive spectral imaging, our group has developed a new class of imagers dubbed the coded aperture snapshot spectral imager (CASSI). CASSI instruments utilize a coded aperture and one or more dispersive elements to modulate the optical field from a scene. A detector captures a two-dimensional, multiplexed projection of the three-dimensional datacube representing the scene. The nature of the multiplexing performed depends on the relative position of the coded aperture and the dispersive element(s) within the instruments.

Dual Disperser CASSI (DD-CASSI)

Associated publication: Gehm et al., "Single-shot compressive spectral imaging with a dual-disperser architecture," Optics Express, October 2007.

 

 

The source is imaged through two sequentially dispersive arms arranged in opposition so that the dispersion in the second arm cancels the dispersion introduced by the first arm. A coded aperture is placed between the two arms. Recovery of the datacube from the detector measurement is performed using an expectation-maximization method designed for hyperspectral images. Such a design applies spatially-varying, spectral filter functions with narrow features. Through these filters, the detector measures a projective measurement of the datacube in the spectral domain. In essence, the DD-CASSI sacrifices spatial information to gain spectral information about the datacube. Spectral information from each spatial location in the scene is multiplexed over a localized region on the detector. A useful property of the design is that the measurement resembles the scene, making it easy to focus the camera on objects in the scene. This also makes it possible to perform local block processing of the detector data to generate smaller datacubes of subsets of the entire scene.

 

DD-CASSI Experimental Prototype

 

Instrument Characteristics
  1. Spectral range of 520-590 nm with a bandpass filter placed at the input to remove out-of-band stray light.
  2. Aperture code based on an order 192 S-matrix.
  3. Equilateral prism used for dispersion as required dispersion is small and a low dispersion grating produces undesirable overlapping orders.
 

DD-CASSI Spectral Image Reconstructions

 

Detector measurement of a ping pong ball illuminated by a 532 nm source

Sum through the reconstructed datacube over the wavelength dimension

Intensity as a function of wavelength through the reconstructed ball

 

 

Detector measurement of a scene consisting of three lemons

Sum through the reconstructed datacube over the wavelength dimension

Intensity as a function of wavelength through each of the three fruits

Single Disperser CASSI (SD-CASSI)

Associated publication: Wagadarikar et al. "Single disperser design for coded aperture snapshot spectral imaging," feature issue on Computational Optical Sensing and Imaging, Applied Optics 47 (10), B44-51 (2008).

 

 

In working with the dual disperser, we realized that we could build a simpler spectral imaging instrument. We called this new design the SD-CASSI instrument, short for a single disperser coded aperture snapshot imaging spectrometer. The instrument essentially consists of an imaging lens that images the scene on to the aperture code and a pair of relay lenses that relay the image from the plane of the aperture code to the detector through a dispersive element placed between them.

Like the DD-CASSI, the SD-CASSI does not directly measure each voxel in the desired three-dimensional datacube. It collects a small number (relative to the size of the datacube) of coded measurements and a sparse reconstruction method is used to estimate the datacube from the noisy projections. The instrument disperses spectral information from each spatial location in the scene over a large area across the detector. Thus, spatial and spectral information from the scene is multiplexed on the detector, implying that the null space of the sensing operation of the SD-CASSI is different from that of the DD-CASSI. Also, a raw measurement of a scene on the detector rarely reveals spatial structure of the scene and makes block processing more challenging.

The SD-CASSI removes the Computed Tomographic Imaging Spectrometer (CTIS) constraints of measuring multiple projections of the datacube and using a large focal plane array. Essentially, just one spectrally-dispersed projection of the datacube that is spatially modulated by the aperture code over all wavelengths is sufficient to reconstruct the entire spectral datacube.

 

SD-CASSI Experimental Prototype

 
   

Instrument Characteristics
  1. Spectral range of 540-640 nm with a bandpass filter placed at the input to remove out-of-band stray light.
  2. Aperture code based on an order 192 S-matrix.
  3. Equilateral prism used for dispersion as required dispersion is small and a low dispersion grating produces undesirable overlapping orders.

 

SD-CASSI Spectral Image Reconstructions

 

 

A scene consisting of a ping pong ball illuminated with a 543 nm green laser and a white light source filtered by a 560 nm narrow band filter (left), and a red ping pong ball illuminated with a white light source (right). Detector measurement of the scene consisting of the two ping pong balls. Given the low lineardispersion of the prism, there is spatio-spectral overlap of the aperture code-modulated images of each ball.

 

 

Spatial content of the scene in each of 28 spectral channels between 540 nm and 640 nm. The green ball can be seen in channels 3 - 8, while the red ball can be seen in channels 23 - 25.
 

(a)

(b)

(a) Spectral intensity through a point on the ping pong ball illuminated with a 543 nm green laser and a white light source filtered by a 560 nm narrow band filter. (b) Spectral intensity through a point on the red ping pong ball illuminated with a white light source. Spectra from an Ocean Optics non-imaging reference spectrometer are shown for comparison.

DD-CASSI vs. SD-CASSI

Since the DD-CASSI only multiplexes spectral information in the datacube, it cannot reconstruct the spectrum of a point source object. On the other hand, the SD-CASSI can reconstruct the spectrum of a point source, provided that the source spatially maps to an open element on the coded input aperture. This implies that for reconstructions demanding high spatial resolution with less stringent demands on spectral resolution, the DD-CASSI instrument should be the compressive spectral imager of choice. On the other hand, where spectral resolution is more critical than spatial resolution in the datacube, the SD-CASSI instrument should be chosen. The SD-CASSI has the additional benefit of requiring fewer optical elements, making optical alignment much easier. The table below summarizes the key differences between the DD-CASSI and SD-CASSI instruments.

DD-CASSI SD-CASSI
  1. 9 optical elements
  2. More difficult to align
  3. No spatial multiplexing, fewer observations
  4. Cannot spectrally resolve point sources
  5. Block processing possible
  6. Instrument of choice for high spatial resolution but lesser spectral resolution
  1. 6 optical elements
  2. Easier to align
  3. More spatial multiplexing
  4. May not spatially resolve point sources
  5. Block processing more challenging
  6. Instrument of choice for high spectral resolution but lesser spatial resolution