This PDF file contains the front matter associated with SPIE Proceedings Volume 8122, including the Title Page, Copyright information, Table of Contents, A Tribute to Joseph W. Goodman plus a Preface from Joseph W. Goodman, and the Conference Committee listing.
We describe a method that we believe will for the first time allow diffraction-limited imaging through ground-level
turbulence with large apertures and at large distances (e.g., 1mm resolution at 1km and at a wavelength of 1μm). The
key lies in collecting image data in the spatial frequency domain via the method of Fourier telescopy and in taking
suitable time averages of the Fourier telescopy signal magnitude and phase. The method requires active illumination of
the target with laser light, and the time averages required will likely be of many seconds duration, if not minutes. The
scheme will thus not be suitable for time-varying scenes.
Building on the work of Goodman and Lawrence , we have extended digital holographic imaging to gigapixel scales
with 2-D aperture synthesis. Sub-pixel registration algorithms were required to mosaic together thousands of arrays of
data, and phase-error correction algorithms were required to correct for system instabilities.
In this talk we present a series of illustrative topics in Fourier Optics that are proving valuable in the design of EDOF
camera systems. They are at the level of final examination problems that have been made solvable by a student or
professoi having studied from one of Joseph W. Goodman's books---our tribute for his 75fr year. As time permits,
four illustrative topics are l) Electromagnetic waves and Fourier optics;2) The perfect lens; 3) Connection between
phase delay and radially varying focal length in an asphere and 4) tailored EDOF designs.
Goodman's popular linear systems formulation of scalar diffraction theory includes a paraxial (small angle)
approximation that severely limits the conditions under which this elegant Fourier treatment can be applied. In
this paper a generalized linear systems formulation of non-paraxial scalar diffraction theory will be discussed.
Diffracted radiance (not intensity or irradiance) is shown to be shift-invariant with respect to changes in incident
angle only when modeled as a function of the direction cosines of the propagation vectors of the usual angular
spectrum of plane waves. This revelation greatly extends the range of parameters over which simple Fourier
techniques can be used to make accurate diffraction calculations. Non-paraxial diffraction grating behavior
(including the Woods anomaly phenomenon) and wide-angle surface scattering effects for moderately rough
surfaces at large incident and scattered angles are two diffraction phenomena that are not limited to the paraxial
region and benefit greatly from this extension to Goodman's Fourier optics analysis. The resulting generalized
surface scatter theory has been shown to be valid for rougher surfaces than the Rayleigh-Rice theory and for
larger incident and scattered angles than the classical Beckman-Kirchhoff theory. This has enabled the
development of a complete linear systems formulation of image quality, including not only diffraction effects and
geometrical aberrations from residual optical design errors, but surface scatter effects from residual optical
fabrication errors as well. Surface scatter effects can thus be balanced against optical design errors, allowing the
derivation of optical fabrication tolerances during the design phase of a project.
The white-light compensated rotational shear interferometer (coherence interferometer) was developed in an effort
to study the spatial frequency content of passively illuminated white-light scenes in real-time and to image sources
of astronomical interest at high spatial frequencies through atmospheric turbulence. This work was inspired by
Professor Goodman's studies of the image formation properties of coherent (laser) illuminated transparencies. We
discovered that real-time image processing is possible using white-light interferometry. The concept of a
quasimonoplanatic approximation is introduced as a parallel to the quasimonochromatic approximation needed to
describe the theory of Fourier transform spectrometers. This paper describes the coherence interferometer and
reviews its image formation properties under the conditions of quasimonoplanacity and describes its development
and its applications to physical optics, optical processing and astrophysics including the search for exoplanets.
We review two techniques of unconventional holography, coherence holography and photon-correlation holography,
which we recently proposed and experimentally demonstrated. We will emphasize the importance of noticing
mathematical analogies in optics and physical phenomena, which give insights into the methodology for developing new
Since VanderLugt's famous 1964 paper showing that complex valued filters for optical matched filters could be
made, an extremely large number of papers have been written - some by me and some by Professor Goodman, and
many more by others. Yet optical Fourier transform filtering is almost never used for anything but university
research. The reasons are fairly well known but seldom stated. We have found one new approach to pattern
recognition that solves most of the problems and introduces a totally new and very useful thing that can be done
with Fourier filtering.
In this presentation we discuss a new type of optical microscope that is capable of obtaining spectral and spatial
information from biological tissue samples. The current system uses multiplexed volume holograms to probe multiple
depths of a tissue sample without the need for scanning. This greatly simplifies the instrument and should allow it to be
adapted for laproscopic applications. The technique can be combined with fluorescent dye markers to identify cancerous
We review the history of scalar diffraction theory from the classical approach of Kirchkoff, Rayleigh and Sommerfeld, to
the modern ideas introduced by Duffieux that eventually led to the use of distribution theory by Arsac , and finally to the
derivation of the expressions using quantum mechanics and relativity. The latter exploits the invariant properties of the
energy-momentum four-vector of light.
Electromagnetic waves carry energy, linear momentum, and angular momentum. When light (or
other electromagnetic radiation) interacts with material media, both energy and momentum are usually
exchanged. The force and torque experienced by material bodies in their interactions with the
electromagnetic field are such that the energy as well as the linear and angular momenta of the overall system
(i.e., the system of field plus matter) are conserved. Radiation forces are now used routinely to trap and
manipulate small objects such as glass or plastic micro-beads and biological cells, to drive micro- and nanomachines,
and to contemplate interstellar travel with the aid of solar sails. We discuss the properties of the
electromagnetic field that enable such wide-ranging applications.
Optical transforms are represented in computers by their discrete versions. In particular, Fourier optics is represented
through Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT). Being discrete representation of the
optical Fourier transform, these transforms feature a number of peculiarities that cast a new light on such fundamental
properties of the Fourier Transform as sampling theorem and the uncertainty principle. In this paper, we formulate the
Discrete Sampling Theorem and the discrete uncertainty principle, demonstrate that discrete signals can be both bandlimited
in DFT or DCT domains and have strictly limited support in signal domain and present examples of such "bandlimited/
space-limited" signals that remain to be so for whatever large of their samples.
Speckle was re-discovered after the invention of the laser in 1960. The unpublished 1963 Stanford Electronics
Laboratory report by J W Goodman was the first comprehensive derivation of the first and second order statistics of the
speckle intensity. This short paper describes how the senior author came to know Professor Goodman through their
mutual, and lasting, interest in laser speckle. New results in speckle continue to be discovered, and we briefly describe
one of these, the elimination of phase vortices using cascade adaptive optics systems.
This paper leverages many successes of the Fourier theorem in modeling the measurable experimental data in the fields
of optical physics while underscoring some of the misinterpretations by focusing on the light-matter interaction
processes, which give rise to the measurable data. We are proposing that we need to introduce Interaction Process
Mapping Epistemology (IPM-E) to complement the currently successful Measurable Data Modeling Epistemology
(MDM-E). We show that IPM-E helps us recognize that EM waves cannot produce interference fringes by themselves as
they do not interact with each other. Accordingly we have been missing the NIW-principle (Non-Interaction of Waves).
Application of the NIW-principle to Fourier theorem, as applied to optical physics reveals and helps us understand many
optical phenomena much better than so far we have understood. We discuss Fourier optics, Fourier transform
spectrometry, coherence theory, spectrometry theory and laser mode locking theory and summarize for each case, the
deeper understanding that we have been missing by neglecting the NIW-principle.
Optical singularities are localized regions in a light field where one or more of the field parameters, such as phase
or polarization, become singular with associated zero intensity. Focused to a small spot, the electromagnetic
field around the singularity has interesting characteristics, in particular when it interacts with matter. The
light scattered by a material object within the strongly varying optical field around the singularity is extremely
sensitive to changes and can be exploited for metrology with high sensitivity and the study of physical processes
on a nanometer scale.
We explore the use of coherent optical processors for visualizing phase-space representations, as well as for
designing complex amplitude masks, which reduce the impact of focus errors on the modulation transfer function
Fundamental Fourier optics is applied to metallic near-field superlens, whose transfer function is computed with the
transfer matrix, the Surface Plasmon Polariton (SPP) resonance and the SPP waveguide theory. However, when the
object nano-structure consists of feature nano-slits and nano-holes etc, which are as the basic object elements to scatter
the light, especially when the objects are metal, the electrical dipoles are induced at the nano-slits and nano-holes by the
illuminating light, the space invariance condition can be not respected within the dimension of the nano-meter scale
objects, so that the point spread function becomes approximate and the superlens is usually characterized by the image
of a two nano-slit pattern. The superlens is designed and optimized based on the transfer function. Improvement in the
transfer function can improve significantly the image quality. The real image of the near-field superlens can be
computed with numerical simulation using the FDTD method.
In this paper we present technical evolution at Physical Optics Corporation (POC), from Fourier Optics, inspired by
Professor Joseph Goodman's classic book: Introduction to Fourier Optics, to recent directions at POC, related to socalled
The theory of partial coherence has a long and storied history in classical statistical optics. The vast majority
of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have
phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear
interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing
quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons,
i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence
tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been
mimicked with classical-state light, questioning wherein lies the classical-quantum boundary. We have shown,
for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive
partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial
coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically
and experimentally, that classical phase-sensitive light produces ghost images most closely mimicking those
obtained with biphotons, and we derive the spatial resolution, image contrast, and signal-to-noise ratio of a
standoff-sensing ghost imager, taking into account target-induced speckle.
Digital holography, Fourier optics and speckle are combined to enable a new direction in drug discovery.
Optical coherence imaging (OCI) is a coherence-gated imaging approach that captures dynamic speckle from inside
living tissue. The speckle temporal fluctuations arise from internal motions in the biological tissue, and the changes in
these motions caused by applying drugs can be captured and quantified using tissue dynamics spectroscopy (TDS). A
phenotypic profile of many reference drugs provides a training set that would help classify new compounds that may be
candidates as new anti-cancer drugs.
In the mid-1990s when digital photography began to enter the consumer market, Professor Joseph Goodman
and I set out to explore how computation would impact the imaging system design. The field of study has since
grown to be known as computational photography. In this paper I'll describe some of its recent advances and
challenges, and discuss what the future holds.