We have developed an analytical model for the design and optimization of common-path interferometers (CPI's) based on spatial filtering. We describe the mathematical analysis in detail and show how its application to the optimization of a range of different CPI's results in the development of a graphical framework to characterize quantitatively CPI performance. A detailed analytical treatment of the effect of curvature in the synthetic reference wave is undertaken. We show that it is possible to improve the linearity and fringe accuracy of certain standard interferometers by a modification of the Fourier filter, and we propose and analyze a dual CPI system for the unambiguous mapping of phase to intensity over the complete input phase range.

Optimal phase contrast in common-path interferometry

We introduce the notion of optimal phase-only filters (OPOFs) that yield improved signal to noise ratios (SNRs). We illustrate the improvement in SNR resulting from the use of OPOFs with the help of several analytical examples and simulation results.

Phase-only filters with improved signal to noise ratio

We present a new approach to obtain superresolved images in digital holography by means of synthetic aperture generation using common-path interferometry and off-axis illumination in optical imaging systems. The paper includes two parts. First, we present a simple approach to double the resolution of an optical system using tilted illumination onto the object and an optical element in the image plane to produce the holographic recording. Then we present a novel approach consisting of attaching a diffraction grating in parallel together with the object in the input plane and using off-axis illumination provided by a Vertical Cavity Surface Emitting Lasers (VCSEL) array to allow us achieving a major improvement in the optical resolution limit with an extremely low penalty in the complexity of the resulting system. Experimental investigation based on commercial microscope objectives is presented.

/pdf/superresolution-optical-system-by-common-path-interferometry-29ugaqn6jb.pdf

Superresolution optical system by common-path interferometry.

https://www.uv.es/~gpoei/articulos/(2008)%20OC%20281%20(17)%202473%20Common-path%20phase-shifting%20digital%20holographic%20microscopy%20A%20way%20to%20quantitative%20phase%20imaging%20and%20superresolution.pdf

Common-path phase-shifting digital holographic microscopy: A way to quantitative phase imaging and superresolution

We introduce a new interferometric setup for single-exposure wide-field holographic phase imaging of highly dynamic biological samples. In this setup, the interferometric signal originates from a specially designed reflective interferometric chamber (InCh), creating an off-axis interferogram on the output plane of the system. The setup only requires the InCh and a simple reflection-mode two lens imaging system, without the need for additional optical elements such as gratings in the beam path. In addition, due to the close-to-common-path geometry of the setup, phase noise is greatly reduced. We experimentally compare the inherent phase stability of the system in ambient conditions to that of a conventional interferometer. We also demonstrate use of this system for wide-field quantitative phase imaging of two different highly dynamic, optically transparent biological samples: beating myocardial cells and moving unicellular microorganisms.

https://www.spiedigitallibrary.org/journals/journal-of-biomedical-optics/volume-15/issue-3/030503/Reflective-interferometric-chamber-for-quantitative-phase-imaging-of-biological-sample/10.1117/1.3420179.pdf

Reflective interferometric chamber for quantitative phase imaging of biological sample dynamics

Common-path interferometers have been used to perform phase visualization for over 40 years. A number of techniques have been proposed, including dark central ground, phase contrast (π/2 and π), and field-absorption interferometers. The merits of the interferometers have been judged ad hoc by either tests with a small number of phase objects or by computer simulation. Three standardized criteria, which consolidate the work of others, are proposed to evaluate common-path interferometers: fringe visibility, fringe irradiance, and fringe accuracy. The interferometers can be described as one generic class of Fourier-plane filters and can be analyzed for all input conditions. Closed-form expressions are obtained for visibility and irradiance under the forced condition that little inaccuracy is tolerated. This analysis finds that the π-phase-contrast interferometer is a good choice if the optical phase disturbance is at least 2π; for smaller disturbances, the Π/2 filter selected by Zernike is near optimum. It is shown mathematically that the resulting fringe visibility is highly object dependent, and good results are not ensured. By allowing the optical beam to be 50% larger than the phase object, the interferometer performs well under all conditions. With this approach and a combination π-phase/field-absorption filter, interference fringe visibility is greater than 0.8 for all phase objects.

Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances.

A device for target scoring includes an elongated retro-reflective member, a first light source, a second light source, a first light sensor, a second light sensor and a processor. The first light source is disposed at a first location and is spaced apart from the retro-reflective member. The first light source is also positioned so as to be able to direct a first beam of light toward the retro-reflective member. The second light source is disposed at a second location spaced apart from both the retro-reflective member and from the first light source. The second light source is also positioned so as to be able to direct a second beam of light toward the retro-reflective member so that the second beam of light intersects the first beam of light over an area so as to define a target area. The first light sensor is disposed adjacent the first light source and is positioned so as to be able to receive light from the first light source that has been reflected from the retro-reflective member. The first light sensor generates a first signal indicative of a first position of a first blockage of illumination from the retro-reflective member. The second light sensor is disposed adjacent the second light source and is positioned so as to be able to receive light from the second light source that has been reflected from the retro-reflective member. The second light sensor generates a second signal indicative of a second position of a second blockage of illumination from the retro-reflective member. The processor is responsive the first signal and to the second signal. The processor is programmed to determine a location of the object in the target area, based on the first position of the first blockage of illumination and the second position of the second blockage of illumination.

Target scoring system

Expectation values in the frequency domain are used to calculate the correlation peak of an optical matched filter These calculations show that the phase-only and classical matched filters are equally sensitive to scale changes when modest high-pass filtering is used Computer simulations were done for verification

Comparison Of Phase-Only And Classical Matched Filter Scale Sensitivity

An acousto-optic correlator for wideband signals. The invention is defined by and relates to device in which a laser beam is split into two paths of a Mach-Zehnder interferometer arrangement. A first Bragg cell of which, modulated with a signal Re{S 1 (t)exp(jw o t)}, receives the first beam that is reflected off a first flat mirror. A second Bragg cell of which, modulated with a signal Re{S 2 (t)exp(jw o t)}, receives a beam that is reflected off a second flat mirror. The undiffracted light from both of the modulators is blocked. The diffracted light emitted from the first and second Bragg cells passes through first and second imaging lenses respectively. The two diffracted light beams are then combined with an angular separation between beams. The combined beam is incident upon a square-law detector array which is at the image plane of the imaging lenses. Due to the square-law detection process, terms of low frequency biases and complex correlation on a spatial carrier develop. This output is filtered to remove the low frequency component. The remaining signal being demodulated by in-phase and quadrature detection techniques. The correlation magnitude and the phase are calculated. This provides for precise temporal resolution.

Acousto-optic time-integrating signal processor

This paper describes an acousto-optic (AO) processor that offers a small, lightweight solution to detecting and analyzing wide-bandwidth, spread-spectrum signals. The processor is being developed for insertion into an existing electronic support measure (ESM) test-bed. The correlator will have a processing bandwidth of 500 MHz and will be used to detect direct- sequence phase modulated (PM) signals, frequency-hopped signals, chirps, and impulse signals. An in-line AO correlator is the heart of the processor and is used for detecting wideband activity. Subsequent digital processing, including Fourier transformation, will be used to determine center frequencies, bandwidths, and band shape. Theoretical operation of the correlator is discussed along with descriptions of the radio frequency (RF) interfaces and digital post-processing.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Christopher Scott Anderson

Papers

Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances.

Target scoring system

Comparison Of Phase-Only And Classical Matched Filter Scale Sensitivity

Acousto-optic time-integrating signal processor

Wideband acousto-optic processor for ESM applications