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# SIGGRAPH 2012 Computational Plenoptic Imaging Course - 3 Spectral Imaging

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SIGGRAPH 2012 Computational Plenoptic Imaging Course - 3 Spectral Imaging

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• Table: formulas from Born &amp; Wolf “Principles of Optics”, 7th ed., p. 450s = slit widthd = spacing between slitsAssume s/d = ¼ as in their figurek = 2pi / lambdaMaxima of diffraction pattern are at p = m lambda / d Evaluate Fig. 8.19 (b) at position of the maximaI = const. * Sin^2(ksp/2) / (ksp/2)^2ksp = 2pi/lambda * s * m lambda /d = pi *s/d * m = pi * ¼ * mThis gives a sequence of numbers S_m and lim_{m \\goesto \\infty } \\sum_{-m..m} S_m = 4The limit lim_{s/d \\goesto 0} I = 1.The percentages in the table are computed w.r.t. this limit. They will change if the ratio of slit width to slit spacing (s/d) is changed. In particular, the diffraction order 4 with 0 intensity results from s/d being a proper fraction 1/4.You can achieve higher light efficiency by moving the peaks closer together , i.e. letting the fraction s/d go to zero, however, then the orders m=1..N move closer together and consequently there is less space for the spectrum -&gt; spectral resolution is decreased.
• 6-filter wheel – Thorlabs Inc. CFW6Big filter wheel – MPI Astronomy – part of the James Web Space telescope(http://www.jwst.nasa.gov/) is MIRI http://www.roe.ac.uk/ukatc/consortium/miri/overview/instrument_design.htmlLCTF (Liquid Crystal Tunable Filter) = programmable wavelength bandpass filter – LOT-Oriel group: http://www.lot-oriel.com/uk/en/home/tunable-filters/
• Wiki page: http://en.wikipedia.org/wiki/Fourier_transform_spectroscopyMain purpose – increase light throughput – multiplexing advantage
• Example: WiFES Wide Field Spectrograph - 3 degrees of an arc fov, extremely large for telesopesImages from http://rsaa.anu.edu.au/research/highlights/wifes-and-fine-art-spectroscopy
• SPIFFI: SPectrometer for Infrared Faint Field Imaginghttp://www.eso.org/sci/facilities/paranal/instruments/sinfoni/inst/instrument.htmlSlicer closeup from:http://www.astro.ufl.edu/~raines/snr-fisica.html
• Development of four-dimensional imaging spectrometers (4D-IS)Nahum Gat, Gordon Scriven, John Garman, Ming De Li, Jingyi ZhangOpto-Knowledge Systems, Inc. (OKSI)
• Also Bodkin design 2006 (res 100x100x20)Snapshot Hyperspectral Imaging – the Hyperpixel Array™ CameraAndrew Bodkin, A. Sheinis, A. Norton, J. Daly, S. Beaven and J. WeinheimerHao Du, Xin Tong, Xun Cao and Stephen Lin. A Prism-based System for Multispectral Video Acquisition. In Proceedings of IEEE International Conference on Computer Vision (ICCV), 2009http://www.cs.washington.edu/homes/duhao/Projects/MultiSpectral/MultiSpectralwebsite.html
• Computed-tomography imaging spectrometer: experimental calibration and reconstruction resultsDescour, M. Dereniak, E. APPLIED OPTICS,1995, VOL 34; NUMBER 22, pages 4817Example from:http://www.optics.arizona.edu/descour/computed.htmRaw image 1024x1024; result 75x75 spatial resolution, 30 spectral bands (around 1997/1998), computed on Pentium II 450 MHz. spectral resolution: \\Delta\\lambda = (710-420) / 30 = 9.6Max R = 74 (at 710)
• 54 slices computed, assuming they are resolved, this gives a max. resolution at 700 nm of \\Delta\\lambda = (666-422) / 54 = 4.5 nmR = 700 / 4.5 = 156
• Gehm et al., &quot;Single-shot compressive spectral imaging with a dual-disperser architecture,&quot; Optics Express, October 2007.Wagadarikar et al. &quot;Single disperser design for coded aperture snapshot spectral imaging,&quot; feature issue on Computational Optical Sensing and Imaging, Applied Optics 47 (10), B44-51 (2008).
• 35 bands, spatial approx. 200x200 pixels (judging from image qaulity, actual resolution appears to be lower be a factor at least two), no specifics provided in paper. SDCASSI (Wagadarikar’08) input image resolution 1040 x 1392 pixels. Result: 128 x 128 x 28 is claimed to be higher spectral res. than DDCASSI above, lower spatial res.
• Spectralization: Reconstructing spectra from sparse dataMartin Rump and Reinhard KleinIn proceedings of SR &apos;10 Rendering Techniques, pages 1347-1354, Eurographics Association, June 2010Xun Cao, Xin Tong, Qionghai Dai and Stephen Lin, &quot;High Resolution Multispectral Video Capture with a Hybrid Camera System&quot;, IEEE international Conference on Computer Vision and Pattern Recognition (CVPR), 2011
• ### SIGGRAPH 2012 Computational Plenoptic Imaging Course - 3 Spectral Imaging

1. 1. Spectral Imaging Ivo IhrkeSaarland University/MPI Informatik
2. 2. The spectral data cube • spectrometer
3. 3. Principle of Operation - Dispersiondisadvantage:• dispersion relation is nonlinearadvantage:• light efficient
4. 4. Diffraction Grating Diffraction Order Percentage of transmitted Light– At center, no diffraction 0 25% 1 20.26%– For higher orders, diffraction is 2 10.13% 3 2.25% taking place 4 0% remainder 9.72% disadvantage: • low light efficiency advantage: • linear relation pixel pos. <-> wavelength
5. 5. Diffraction-Based Systems– Diffraction-based example ->– Spectrometer calibration (all types)1. mapping pixel <–> wavelength2. relative intensity of wavelengths
6. 6. The spectral data cube• Spatial Scanning • E.g. in satellite imaging (2D sensor) – Pushbroom scanning
7. 7. Spatial Scanning • Generalized Mosaics [Schechner & Nayar] • linear filter • each pixel column filtered differently • rotational motion & registration to assemble image stack
8. 8. The spectral data cube• Spectral scanning
9. 9. Frequency Scanning • Michelson Interferometer with moving mirror - Fourier Transform Imaging Spectroscopy (FTIS)
10. 10. Imaging SpectrometersThe quest for the instantaneous spectral data cube (4D Imaging)
11. 11. Multiplexing - Image slicers[WiFeS – Wide FieldSpectrometer]
12. 12. Multiplexing - Image slicers[SPIFFI - SPectrometer forInfrared Faint Field Imaging]
13. 13. Fiber Optical cables (OKSI)300 “pixels”2D -> 1D reformatting
14. 14. Multiplexing: Prism-Mask Based System [Du’09]
15. 15. Computational Imaging SpectrometersThe quest for the instantaneous spectral data cube
16. 16. CTIS –Computed Tomography Imaging Spectrometry • Original method [Descour’95] • Image a full diffraction pattern • Perform “CT” spectral image diffraction pattern
17. 17. CTIS in graphics • HDR imaging for CTIS [Habel’12] (not snapshot due to HDR exposure stack)
18. 18. CTIS in graphics • Spatial resolution 124x124, 54 bands [Habel’12]
19. 19. CASSI – Coded Aperture Snapshot Spectral Imaging
20. 20. CASSI – Coded Aperture Snapshot Spectral Imaging Implementation with prisms
21. 21. CASSI – Coded Aperture Snapshot Spectral Imaging • Resolution: spatial ~200 x 200 pixels spectral ~30 bands projection reconstruction (stack) spectra
22. 22. Spectral Transfer • Transfer low-res spectra to high res RGB image [Rump’10,Cao’11]
23. 23. Applications
24. 24. Applications • automatic white balancingSpatially uniform illuminationraw from RGB tungsten WB `greyworld WB spectral WB spectra Spatially varying illumination [Cao11]
25. 25. Applications • improved tracking RGB – spectral – tracking lost tracking OK • real and fake skin detection [Cao11]
26. 26. Applications • analyze / restore paintings [Calit]
27. 27. Applications • Satellite-Based Remote Sensingvegetation mapping urban land use pollution monitoring [DigitalGlobe’10]
28. 28. • Multispectral at Siggraph’12 – Kim, Harvey, Kittle, Rushmeier, Dorsey, O’Prum, and Brady “3D Imaging Spectroscopy for Measuring Hyperspectral Patterns on Solid Objects”, Monday, 3:45 - 5:35 – “Appearance” – Hosek and Wilkie, “An Analytic Model for Full Spectral Sky-Dome Radiance”, Wednesday 3:45-5:35 pm – “Physics and Mathematics for Light”