Paper Summaries

Fourier Optics Papers and Others

These works are related to optical image processing using Fourier optics. This list was originally made for Gordon's contrast reduction project, so not all papers are Fourier optics papers. This list was made on January 17, 2008.

Zernike Phase Contrast

It might be helpful to reference the original Zernike Phase Contrast method.
* Zernike, F. "Diffraction theory of knife-edge test and its improved form, the phase-contrast method," Royal Astronomy Society Monthly Notices: 94, 377-384, 1934.

All-optical spatial filtering with power-limiting materials

Chandra Yelleswarapu, Pengfei Wu, Sri-Rajasekhar Kothapalli, D.V.G.L.N. Rao, Brian Kimball, S. Siva Sankara Sai, R. Gowrishankar, S. Sivaramakrishnan
Optics Express 2006
Forward References: 0
http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-4-1451

OBJECTIVE: edge enhanced images, control enhancement with input intensity
HOW: Put nonlinear material in Fourier plane to act as high pass filter. The nonlinear material absorbs high intensities and allows lower intensities below a power-limiting threshold to pass. Since low frequencies have high intensities, they are absorbed while lower intensity high frequencies are transmitted. When the input intensity is above the power-limiting threshold, a high pass filter is created and the edge enhancement can be controlled by increasing input intensity.
OPINION: Edge image results are pretty good (compared to what I've seen in other papers). This paper is worth looking at even though it doesn't have any forward references yet. Previous work included the necessity of aligning other beams into the Fourier plane with careful attention to overlap of the two beams for frequency selection (not so easy!, and problematic).

All-optical image processing by means of a photosensitive nonlinear liquid-crystal film: edge enhancement and image addition-subtraction

M.Y. Shih, A. Shishido, I.C. Khoo
Optics Letters 2001
Forward References: 7
http://www.opticsinfobase.org/abstract.cfm?&id=64908

OBJECTIVE: edge enhancement, image addition-subtraction
HOW: Put twisted PNLC (photosensitive nonlinear liquid-crystal) in F. plane. The high intensities of lower frequency components induce a polarization change in the PNLC making them have different polarization than the high frequency components. An analyzer (polarizer) controls the selection of frequencies and therefore edge enhancement. Image addition and subtraction are performed with a different setup (not Fourier optics) using INcoherent linearly polarized light and the PNLC sample. Signals A and B have different polarizations and are sent through the crystal. The angle of the polarizer on the output side of the crystal determines whether A and B are added or subtracted.
OPINION: This paper also seems nice, but I think the previous paper (which references this one) has slightly better edge results. The author I.C. Khoo has multiple papers in this area, which probably gives an indication of the quality of the work.

SIMILAR PAPER: All-optical neural-net-like image processing with photosensitive nonlinear nematic film

I.C. Khoo, K. Chen, A. Diaz
Optics Letters 2003
Forward References: 0
http://www.opticsinfobase.org/abstract.cfm?id=78022

OBJECTIVE: perform neural-net-like image processing optically. such as edge enhancement.
OPINION: This paper seems the same as his previous work; it's the same setup. I think he's just making the claim that the system can do neural-net-like image processing. I wouldn't really look at this.

All-optical image processing with a supranonlinear dye-doped liquid-crystal film

M.Y. Shih, A. Shishido, P.H. Chen, M.V. Wood, I.C. Khoo
Optics Letters 2000
Forward References: 3
http://www.opticsinfobase.org/abstract.cfm?&id=62054

OBJECTIVE: invert image intensities
HOW: Put nonlinear dye-doped nematic liquid crystal in F. plane to act as a phase modulation element. Amplitude modulation in the output signal is achieved by increasing the input beam power or using an external control beam. As the signal power is increased, the output goes from being a copy of the input to an inverted version of the input.
OPINION: Results show transition from input to inverted image. This work is also nice, but I would reference Yelleswarapu's "power-limiting material" paper over this one.

Programmable birefringent lenses with a liquid crystal display

Jeffrey Davis, Garrett Evans, Karlton Crabtree, Ignacio Moreno
Applied Optics 2004
Forward References: 0
http://www.opticsinfobase.org/abstract.cfm?URI=ao-43-34-6235

OBJECTIVE: create birefringent lens. add/subtract image for edge enhancement/blurring.
HOW: Not Fourier optics. Display a programmable diffractive lens on the LCD. Put LCD in back of normal glass lens. The LCD is vertically polarized, so for one polarization the lens+LCD becomes a lens combination, and for the other polarization only the glass lens affects it. This causes the object to be focused onto two image planes with different polarizations. A camera takes images focused at a single depth, so it captures a combination of the focused and blurred images of the same object. Since the focused and blurred images of the same object have different polarizations, a polarizer can be inserted into the path to control the addition/subtraction of the two images.
OPINION: Even though this paper does not use Fourier optics, it is interesting because it optically adds/subtracts focused and blurred versions of the same object. Figure 5 shows a) focused, b) blurred, c) addition, d) subtraction. The addition is edge blurring; the subtraction is edge enhancing. I don't know if this paper fits into your related work section though.

Detail-Preserving Contrast Reduction For Still Cameras

Prasanna Rangarajan, Panos Papamichalis
IEEE Intl. Conf. on Img. Proc. 2006
http://ieeexplore.ieee.org/iel5/4106439/4106440/04107172.pdf?tp=&arnumber=4107172&isnumber=4106440

ABSTRACT: This paper describes a detail-preserving contrast reduction technique for images with excessive illumination variation. In an attempt to preserve detail, an image is first separated into its illumination and reflectance components, by a partial differential equation. The illumination component is then scaled to globally reduce contrast. This enhances the perception of detail in the dark areas but at the expense of losing detail in the bright areas. The proposed approach minimizes this loss of detail using a novel recombination strategy. Additionally, the present algorithm preserves colors, avoids halo artifacts, and can be embedded into existing still-camera pipelines.

Adaptive optics with advanced phase-contrast techniques. I. High-resolution wave-front sensing.

Mikhail Vorontsov, Eric Justh, Leonid Beresnev
J. Opt. Soc. Am. A 2001
Forward References: 8
http://www.opticsinfobase.org/abstract.cfm?URI=josaa-18-6-1289

OBJECTIVE: high resolution phase-contrast wavefront sensors. contrast enhancement.
HOW: Based on the Zernike phase contrast method. They present 3 new sensor designs: differential, nonlinear, and optoelectronic Zernike filters. They also incorporate an intensity thresholding with the optoelectronic Zernike filter to further increase contrast. Intensity thresholding: "The phase is shifted by pi/2 for all spectral components q that satisfy I(q) >= 0.75*max(I(q))."
OPINION: This paper is part 1 of 2 parts. It looks like it is significant work in this area since it is a two-part paper with forward references on each part. This is a good reference if you're looking for a recent work on phase-contrast techniques.

SIMILAR PAPER: Adaptive optics with advanced phase-contrast techniques. II. High-resolution wave-front control

Eric Justh, Mikhail Vorontsov, Gary Carhart, Leonid Beresnev, P.S. Krishnaprasad
J. Opt. Soc. Am. A 2001
Forward References: 7
http://www.opticsinfobase.org/abstract.cfm?id=64351

OBJECTIVE: correct wavefront phase
HOW: Capture wavefront with sensor created in the Part I paper. Use gradient flow optimization to determine the correction phase. Display the correction phase on an SLM in the adaptive system.
OPINION: I wasn't too impressed with the resulting phase correction images.

Spatial phase-shift interferometry - a wavefront analysis technique for three-dimensional topometry

Shay Wolfling, Emmanuel Lanzmann, Moshe Israeli, Nissim Ben-Yosef, Yoel Arieli
J. Opt. Soc. Am. A 2005
Forward References: 1
http://www.opticsinfobase.org/abstract.cfm?URI=josaa-22-11-2498

OBJECTIVE: measure surface of object, generate height fields.
HOW: Insert an "optical manipulator (OM) such as a liquid-crystal-based device" in F. plane. The OM modulates amplitude and phase in F. domain in a binary mask way. The camera captures images for different modulations of amplitude and phase. Depending on the F. plane modulations, the images have different intensities for different surface heights. Put these images together to get object surface and height field.
OPINION: This paper might be interesting because it modulates amplitude as well as phase (in contrast to the Vorontsov papers above). Moreover, you can see the contrast differences in the image results in Figure 8.

Medical image processing using transient Fourier holography in bacteriorhodopsin films

Sri-Rajasekhar Kothapalli, Pengfei Wu, Chandra Yelleswarapu, D.V.G.L.N Rao
Applied Physics Letters 2004
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APPLAB000085000024005836000001&idtype=cvips&gifs=yes

OBJECTIVE: real time image processing, display selected spatial frequencies.
HOW: Fourier holography on bR film. (I don't quite understand Fourier holography, so this explanation won't be too clear.) There are two beams, one object beam and one reference beam. The bR film is located in the F. plane, where the two beams join together. The intensity of the reference beam is used to select spatial frequencies. When the object beam is blocked, an edge enhanced image is shown. An edge-softened image is shown when the reference beam is blocked.
OPINION: I'm not sure if this is a good reference. Yelleswarapu is an author on this paper (as well as the "power-limiting material" paper which references this one).

Optical scatter imaging: subcellular morphometry in situ with Fourier filtering

Nada Boustany, Scot Kuo, Nitish Thakor
Optics Letters 2001
Forward References: 8
http://www.opticsinfobase.org/abstract.cfm?URI=ol-26-14-1063

OBJECTIVE: detect wavelength-scale particle sizes
HOW: Dark field imaging technique. Put a variable iris with a center stop in F. plane. It blocks transmitted light to obtain an image of the scattered light.

Fractional derivatives - analysis and experimental implementation

Jeffrey Davis, David Smith, Dylan McNamara, Don Cottrell, Juan Campos
Applied Optics 2001
Forward References: 7
http://www.opticsinfobase.org/abstract.cfm?URI=ao-40-32-5943

OBJECTIVE: edge enhancement, examination of phase objects
HOW: Theoretical proof: mask D in Fourier plane represents the fractional derivative operator. The output is the superposition of two electric fields whose interference allows phase object imaging. Mask parameters can be changed to control which edge (in a 1D rect example) is emphasized more or less. A specific case of the fractional derivative operator is the fractional Hilbert operator.
OPINION: This paper is mainly theoretical. The experimental results are for a 1D rect example. Their 2D analysis is for the radially symmetric case. I don't think this paper has substantial practical results.

Spatial amplification: an image processing technique using the selective amplification of spatial frequencies

Tallis Chang, John Hong, Pochi Yeh
Optics Letters 1990
Forward References: 1
http://www.opticsinfobase.org/abstract.cfm?URI=ol-15-13-743

OBJECTIVE: amplify spatial frequencies instead of blocking frequencies as in spatial filtering
HOW: Put photorefractive crystal (BaTiO3) in F. plane. Align a pump beam to join the object beam in the F. plane. The spatial overlap of the pump beam and object beam determines the frequencies to amplify.
OPINION: This is a really bad paper. The idea seems problematic and not for practical use. The results are limited to filtering in the horizontal and vertical directions. They claim the setup is good for a cascading system, but they don't have experimental results to support that. In a practical sense, the setup with 2 beams overlapping to select spatial frequencies seems inexact; they don't talk about alignment of the beams to select spatial frequencies. The paper itself seems very elementary because it talks about basic concepts of spatial filtering that I thought were known already by 1990.

SIMILAR PAPER: Optical image processing by matched amplification

Tallis Chang, John Hong, Scott Campbell, Pochi Yeh
Optics Letters 1992
Forward References: 0
http://www.opticsinfobase.org/abstract.cfm?URI=ol-17-23-1694

OBJECTIVE: amplify selected frequencies of an image
HOW: Uses spatial amplification from previous paper. One beam contains an image while the other beam contains a selected part of the image. When the beams meet in the F. plane, the selected frequencies from the partial image are amplified. The result should be the original image with the selected part amplified.
OPINION: This doesn't work. This paper is even worse than the original spatial amplification paper. The results are really bad. The idea concept is problematic. The spatial frequencies of the selected image region are amplified instead of the spatial region itself. Processing in the frequency domain will do that (obviously!). For example, they have an image with some lines of text. They use the letter 'w' as their selected image region on the second beam, and they expect the output to amplify all the w's. Of course, frequencies from the letter w are present in other letters, and those other letters will be amplified as well. They try to perform a spatial operation in the frequency domain, and then spend a whole column and a half explaining why it didn't work as they expected. I thought this was common knowledge about frequency domain filtering by 1992.

Optical image encryption based on input plane and Fourier plane random encoding

Philippe Refregier, Bahram Javidi
Optics Letters 1995
Forward References: 89
http://www.opticsinfobase.org/abstract.cfm?URI=ol-20-7-767

OBJECTIVE: encrypt/decrypt images optically, convert images to/from stationary white noise
HOW: To encrypt the image, multiply the image with a random noise phase mask, n, in the input plane. Then put another random noise phase mask, b, in the Fourier plane. The output is an encrypted complex image with amplitude and phase. To decrypt the image, put the encoded complex image in the input plane and the random noise phase mask, b, in the F. plane. The output when imaged onto a CCD is the decrypted image since the CCD will capture the squared magnitude of the output beam.
OPINION: This paper is truly a significant and influential paper in this field. 89 forward references! It has become a standard in the field of optical encryption.

Email from Tom Grycewicz (Jan 17, 2008)

Tom Grycewicz is currently at The Aerospace Corporation in the Sensor Engineering and Exploitation Dept. His work is in optical engineering with quite a bit of work on optical correlators and more generally, optical system modeling and design (image chain analysis), and pattern recognition. I had asked him what he thought were some significant and preferably recent contributions in Fourier optics applied to image processing. This is part of his email response.

Here is the basic problem with image processing: in order to pass data through an optical processing system, the data first needs to be transferred to a spatial light modulator, and this bottleneck is about ten Mpixels per second. Reading the answer requires a camera--another ~ten Mpixel per second bottleneck. A good math coprocessor can handle a Mpixel FFT faster than the data transfer rate to or from the optical system. Add to this all of the advantages a programmable processor has over analog hardware for computing.

Fingerprint recognition was an "almost ran" application. A company in Canada developed and marketed a product which used an optical processor (using an optical binary phase-only Fourier-plane filter) for a commercial system in ~1993. I don't remember the company, the key engineer was Colin Soutar. He published a few SPIE conference papers. But the technology was quickly surpassed by all-digital processing, like the recognition system included in the IBM ThinkPad laptop.

The closest successful application of Fourier optical processing to image analysis I can think of is Fourier transform infrared (FTIR) spectroscopy This process allows a two-dimensional focal plane to capture a three-dimensional hyperspectral data cube. Many instruments of this type have been built, but I don't have references at my fingertips. A good example of the technology is the SPIRE instrument on the ESA Hershel space telescope.

An implementation of wavefront sensing used for Extreme Adaptive Optics (ExAO) uses a pinhole to spatially filter the input wavefront so that high-spatial frequency modes are not sent to the Shack-Hartmann wavefront sensor. The idea first surfaced around 2004. I think the inventor was Lisa Poyneer at Lawrence Livermore National Lab. Of course, this is considered an application of simple optics, not optical processing. Applications of holography to optical memory shows a lot of promise. Readout of a multilayer disk is essentially a holographic process. But of course no good engineer would mention optical disk readout and optical processing in the same breath. Optical processing is the technology of the future....and by unwritten agreement always will be.

Scalar Wave Optics, Time-Frequency Analysis, Wigner transform (Lukas)

Wigner and the LCT

Space-bandwidth product of optical signals and systems

Authors Adolf W. Lohmann, Rainer G. Dorsch, David Mendlovic, Zeev Zalevsky, and Carlos Ferreira
Journal Year JOSA A, Vol. 13, Issue 3, pp. 470-473 doi:10.1364/JOSAA.13.000470
Forward References: n
link http://www.opticsinfobase.org/abstract.cfm?URI=josaa-13-3-470

OBJECTIVE:
HOW:
OPINION: Short, informative paper on Space bandwidth product (SW) for optical signals. Argues that SW as a single number does not fully describe the situation as it denotes the energy (area in Wigner space) of the signal. However, some transforms (affine) may change the shape of the signal in Wigner space, but preserve area. Thus changing the ratio of the spatial / angular sampling, and effectively clipping the signal if kept constant. An argument for doing optical signal processing with Light Fields. Also shows the inversion I was talking about. Will it work on a LF?

Generalizing, optimizing, and inventing numerical algorithms for the

fractional Fourier, Fresnel, and linear canonical transforms Bryan M. Hennelly and John T. Sheridan
JOSA A, Vol. 22, Issue 5, pp. 917-927 doi:10.1364/JOSAA.22.000917
Forward References: n
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-5-917

OBJECTIVE:
HOW:
OPINION: Builds on Lohmann et al. (see above) Tying together the Linear Canonical Transform (LCT) with some general fist order operations on a complex valued distribution. This corresponds to matrix optics of the LF / Wigner distribution function. Shows how the sampling requirement changes as the bounding box of the WDF is transformed by the LCT matrix operations. Thus showing the effect of different transform while staying in 2D. Discuss the SW of some know transforms and methods.

Note - Related paper from the same authors with a Fast LCT in the same issue: Fast numerical algorithm for the linear canonical transform Bryan M. Hennelly and John T. Sheridan JOSA A, Vol. 22, Issue 5, pp. 928-937 doi:10.1364/JOSAA.22.000928 http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-5-928

Don't know if necessary as the LCT matrices can be decomposed into already fast algorithms?

Digital Holography, general

Digital recording and numerical reconstruction of holograms

Ulf Schnars and Werner P O Juptner
Measurement Science and Technology. Vol. 13, no. 9, pp. R85-R101. Sept. 2002
Forward References: n
http://www.iop.org/EJ/article/0957-0233/13/9/201/e209r1.pdf?request-id=b3985

a6b-84cb-4970-aacc-9f2302a68f55

OBJECTIVE:
HOW:
OPINION: Review article introducing digital holography and a couple of applications (shape measurement and microscopy). Shows Fresnel transform - both one direct Fourier and convolution. Shows analytic FT of convolution kernel. Mentions reconstruction scaling introduced by direct method.

Free-space beam propagation between arbitrarily oriented planes based on

full diffraction theory: a fast Fourier transform approach N. Delen and B. Hooker
JOSA A, Vol. 15, Issue 4, pp. 857-867 doi:10.1364/JOSAA.15.000857
Forward References: n
http://www.opticsinfobase.org/abstract.cfm?URI=josaa-15-4-857

OBJECTIVE:
HOW:
OPINION: Quite nice paper showing how to perform Raylight-Sommerfeld diffraction between non parallel planes using the angular spectrum of plane waves. A general complex valued distribution in a plane can be viewed as a spectrum of plane waves through a Fourier transform. A rotation of the plane in 3D space is equivalent to transforming the Fourier coefficients.

Phase-shifting digital holography

Ichirou Yamaguchi and Tong Zhang
Optics Letters, Vol. 22, Issue 16, pp. 1268-1270 doi:10.1364/OL.22.001268
References: n
link http://www.opticsinfobase.org/abstract.cfm?URI=ol-22-16-1268

OBJECTIVE:
HOW:
OPINION: Well known phase-shifting paper where the authors show how to reconstruct phase and amplitude from four holograms with shifted phase (pi/2). They reconstruct the phase fully and thus have the complex valued distribution instead of the intensity valued holographic interference. Newer and older papers (especially in interferometry) exist, but this one is accessible and is targeted especially at holograms. Note - The four phase recordings algorithm is only one of a family, though not mentioned in this paper.

Frequency analysis of digital holography

Thomas M. Kreis
Opt. Eng., Vol. 41, 771 (2002); doi:10.1117/1.1458551
Forward References: n
http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=OPEGAR0000

41000004000771000001&idtype=cvips&gifs=yes

OBJECTIVE:
HOW:
OPINION: Commonly cited paper by Kreis where he analyses the effect of sampling a digital hologram. Basically a frequency analysis of the effects of pixel size and fill factor.

Note - I recently became aware of a comment to this paper, but have not had time to look at it closer: Effect of the fill factor of CCD pixels on digital holograms: comment on the papers "Frequency analysis of digital holography" and "Frequency analysis of digital holography with reconstruction by convolution" Opt. Eng., Vol. 42, 2768 (2003); doi:10.1117/1.1599841 Cheng-Shan Guo, Li Zhang, Zhen-Yu Rong, Hui-Tian Wang

Literature, review, and overview papers

Diffraction and Holography from a Signal Processing Perspective

L. Onural and H. M. Ozaktas HOLOGRAPHY Conference, 2005 Forward References: n
link

OBJECTIVE:
HOW:
OPINION: Not a great paper in itself; basically expresses the LCT (or form there of) as a Fractional Fourier Transform. However: the list of references has some good pointer to overview papers, classical papers, and 'recent' (late 1990 - ~2005) work in signal processing for optics. Not an extensive list, but once a some of the self references are washed out (although there are important work from Onural and Ozaktads in there), some good work remains. E.g: Papoulis, Sherman, Delen and Hooker, Lohmann, Kreis, Wolf, and some others. Have not read all of them.

Computer generated holograms: an historical review

G. Tricoles
Applied Optics, Vol. 26, Issue 20, pp. 4351-4357 doi:10.1364/AO.26.004351
http://www.opticsinfobase.org/ao/abstract.cfm?uri=ao-26-20-4351

OBJECTIVE:
HOW:
OPINION:Bit over 20 years old, so it is dated and lacks much of modern development in CGH. It is however a brief introduction to the general problem of CGH and has an extensive literature list.

Three-dimensional imaging and processing using computational holographic

imaging Yann Frauel, Thomas J. Naughton, Osamu Matoba, Enrique Tajahuerce, and Bahram Javidi
Proceedings of the IEEE, March 2006, Volume: 94, Issue: 3, 636-653, ISSN: 0018-9219
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1605208

OBJECTIVE:
HOW:
OPINION: An overview paper that describes the state of the (authors') research in computational holography at about 2006.OK introduction to the field, and to different applications and problems; compression, encryption, object recognition.