• Lukas reading list on Wave optics, holography, time-frequency analysis

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

Wigner and the LCT

Space-bandwidth product of optical signals and systems

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

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.

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-5-928

Digital Holography, general

Digital recording and numerical reconstruction of holograms

http://www.iop.org/EJ/article/0957-0233/13/9/201/e209r1.pdf?request-id=b3985

• 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

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

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

http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=OPEGAR0000

• 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.

Literature, review, and overview papers

Diffraction and Holography from a Signal Processing Perspective

• 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

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

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.