The "spot of Arago" has been a controversial topic since its inception in 1818 when Poisson predicted its existence, which violated common sense, in an attempt to discredit Fresnel's wave theory of light. Arago performed the experiment and found the surprising prediction was true, thus putting Fresnel's theory on a firm technical foundation. In recent years, the spot of Arago, which exists as a bright spot at the center of the geometrical shadow of a circular obstruction, has caused substantial grief in various high energy laser applications and has come to be considered more of a nuisance than a curiosity. This paper suggests that the size and shape of the spot of Arago is characteristic of the wavefront aberrations of the incident beam and can therefore be used to advantage as a beam sample for wavefront analysis of annular beams. The implementation of this wavefront sampling scheme would eliminate the requirement for a special beam sampling optical component and thus reduce to a minimum the deleterious effects upon the beam frequently accompanying the use of such components. Both experimental and numerical results will be presented along with a discussion of the capabilities and limitations of this particular beam sample for performing various wavefront sensing functions.

ACCOS V is an optical design and analysis program copyrighted by SC, Inc. of Fishers, NY. MCI is a wavefront and interferogram analysis program developed by UNM personnel. These programs have been linked on the Cray and CDC computers at Kirtland AFB. We present information on the use and capabilities of this arrangement, showing examples of ACCOS input and optical path difference (OPD) calculations, and what features MCI adds to ACCOS analysis. Included are Zernike wavefront coefficients [1,2], contour plots, OPD maps, and some new developments in the capabilities of MCI.

The Laser Optical Train Simulation (LOTS) computer program was developed for the Los Alamos National Laboratory laser fusion program. LOTS was built to do end-to-end physical optics analysis of the laser train. LOTS uses a 64 x 64 computer array to describe the complex amplitude distribution of the laser beam. Calculations in LOTS consist of optics operations and data display of the laser beam array. LOTS models diffraction propagation, component aberration, apertures, nonlinear gain or absorption media, lenses and mirrors. It is designed for interactive use and has a user oriented command language which greatly facilitates learning to use the program and problem set-up time. LOTS has been used for a variety of projects since its first version in 1976. These projects include Helios, Antares, the free electron laser, and laser isotope separation at Los Alamos, and LODE and MRAT at the Air Force Weapons Laboratory.

This paper is an overview of recent work of the Lockheed Palo Alto Research Laboratory on the use of subaperture test optics to evaluate the performance of large optical systems. Supported by selected subscale experiments, a theory has been developed that addresses two test conditions, each based on the use of a known test flat in a double-pass configuration with a collimated optical system of unknown quality. The two test conditions, in order of increasing theoretical complexity, are: (1) a single test flat covering only a portion of the full-system aperture, and (2) multiple (not necessarily coherent) test flats. Analyses predict limited utility of a single test subaperture as a function of a subaperture size and location, and aberration content. Multiple subapertures viewing the full system are shown to give good results for higher order aberrations even when the individual test flats are unphased and contain large relative tilt errors. The test techniques described here are fully scalable to future optical systems of arbitrary size. This paper summarizes the theoretical basis for subaperture testing, gives quantitative performance predictions for some selected cases, and presents the results of supporting experimental work.

A method of obtaining surface figure error information from several subaperture interferograms is analyzed, and the effects of roundoff error, digitization error, and fit error are presented. A computer simulation for testing a large flat is shown. This method is applied to average several undersampled interferograms and to analyze lateral shearing interferograms.

Recent work on optimal reconstruction of wavefronts from slope measurements has developed methods based on more realistic models of sensor devices. These methods also resolve certain ambiguities present in earlier reconstruction methods. In the present paper, these methods are applied to sensor configurations which have been proposed in the literature and the errors in estimating and correcting wavefronts are compared.

Phase retrieval implies extraction of the phase of a complex signal from its modulus. In the context of wavefront sensing, the unknown wavefront is represented as a phase across an aperture and the observable is the modulus of the diffracted light, measured in a convenient image plane. In this paper we give a concise statement of the problem, review some proposed solutions, discuss the question of uniqueness, give elementary examples of phase retrieval, and show how the concept might be used in an imaging context.

Precomputable (Cramer-Rao) lower bounds for the integrated mean-square error are presented for the phase retrieval problem. The results are based upon the assumption that the phase is a sample function of a Gaussian random process and that the intensity measurements include additive white Gaussian noise. The bound, which is obtained from an information kernel which is the solution to a Fredholm integral equation, clearly demonstrates the effect of prior statistics, measurement noise and the nature of the linear transformation introduced prior to detection. Several examples are given; in particular, the role of diffraction is shown to be quite important for successful phase retrieval. Finally, the results are extended to include independent measurements of intensity in several planes.

A phase retrieval technique utilizing a differentiation filter in a coherent processing system has been developed and tested. The image irradiance produced in this system is quadratic in the partial derivative of object phase with respect to an object coordinate parallel to the transmittance gradient of the filter. Given a properly chosen set of such image irradiances it is possible to solve for the object phase.

The role played by diffraction in the question of the uniqueness of phase retrieval from intensity measurements in the aperture plane and focal plane of a thin lens is investigated. It is shown for a specific example that diffraction from the lens aperture stop reduces the nonuniqueness which is present if this diffraction is ignored.

On-orbit wavefront sensing and active alignment control are essential features of many spaceborne optical systems currently being developed. Phase retrieval is an especially appropriate wavefront sensing technique for this application, because it directly monitors system image quality and eliminates or reduces the need for auxiliary wavefront sensors. Although the general phase retrieval problem is highly complex and requires sophisticated nonlinear estimation techniques, properly selected linear methods provide satisfactory and efficient solutions to a number of important special cases. This paper discusses the performance of several such linear phase retrieval algorithms. One method yields noise-optimal estimates of small wavefront errors, while a second approach can be used with arbitrarily large errors but is much more sensitive to noise. These two phase retrieval algorithms are actually special cases of a general linear algorithm that can be tuned as a function of wavefront error characteristics, measurement noise statistics, and focal plane detector geometry.

An image-based indirect wavefront aberration estimation which is noise optimal is presented. The minimum variance estimation is obtained by linearizing the focal plane intensity distribution in terms of the aberration parameters and a known set of derivatives of the point spread function. The technique was also made to work successfully for unknown extended sources by Fourier transforming the image to the frequency space. The results obtained from a computer simulation show excellent noise rejection. With a signal-to-noise ratio of 5, the wavefront correction is achieved down to 0.1 λ. In some cases, this method worked when the initial signal-to-noise ratio was less than one. Since the estimation is performed with a linear approximation, the dynamic range of operation was found to be limited to 0.35 RMS λ.

Adaptive optics is gaining acceptance as a method of reducing the degrading effects imposed on optical signals by atmospheric turbulence. One of the critical components of an adaptive optical system is the wavefront sensor, the device which measures the aberrations on the wavefront. The wavefront sensor specifications depend on the mission for which the adaptive optical system will be used and the conditions under which it will operate. Typical missions and operating conditions in which adaptive optics can be used will be presented. The error sources in a wavefront sensor will be discussed in relation to mission and operating conditions. Desirable properties of wavefront sensors will be presented. In the next section the concept of adaptive optics is briefly introduced.

A modified Smartt point-diffraction interferometer employing phase-shifting electronic phase measurement techniques is described. Special techniques making it possible for the interferometer to give good visibility interference fringes for a large range of input wavefront tilts are discussed. A trade-off between acceptable values of wavefront tilt and light efficiency is presented.

The linear-scanned-array wavefront sensor extends the applicability of imaging centroid trackers to Hartmann-type outgoing wave beam-control systems. Oscillating mirrors are used to produce optical integration of the irradiance distribution along one axis while the centroid is measured along the orthogonal axis. The use of linear detector arrays reduces the total detector-element count and increases the measurement bandwidth in comparison to area array sensors. Experiments with a four-beam laboratory model of the sensor have demonstrated centroiding of 150-pm diameter Hartmann spots to an accuracy of better than 0.6 µm at 4-kHz bandwidth. Optimal thresholding can improve the measurement accuracy considerably. The linearity of the sensor was measured to be better than 0.2 pm over an 80-pm range.

We have developed two alignment techniques for optical systems in space, i.e., OYSTER and EEOD. The OYSTER technique is based on wavefront slope. The EEOD technique is based on a star image. This paper discusses the basic algorithms used and the experimental results obtained.

Transfer of optical power from ground-to-space at short wavelengths requires an adaptive wavefront corrector and a sensitive wavefront analyzer. In the several applications envisioned, coherent radiation from a laser beacon or retroreflector and ground based illuminator will be available for wavefront sensing. The superheterodyne wavefront analyzer can therefore be employed for performance approaching the quantum limit. The basics of the superheterodyne approach are discussed and its performance as a wavefront analyzer reviewed.

A sensor system capable of simultaneously measuring phase at 64 discrete points has been developed for use with the digital heterodyne interferometer. With this, two dimensional optical path difference maps of high speed phenomena can be obtained. Featured in this system are 64 channels of phase detection with each channel being provided with a dedicated memory 16 bits wide and 4096 words deep. The system operates at a 100 kHz sample rate and has a sensitivity of 1/300 of a wave rms. A novel method of post priori removal of the corrupting motions of the interferometer optics was demonstrated, allowing high fidelity measurements to be obtained in an unstabilized environment.

An electromechanical focus sensing technique for isolated point or small spot images is described. The technique is a mechanization of the Foucault knife-edge test, and it works with either laser or white light. The focus sensor provides an output voltage vs. focus discriminant which is linear in the vicinity of the best focus and monotonic over a wide range, making it suitable as a sensor for servo focus control applications. The focus sensor uses a chopping wheel at the optical focus and a field lens and bicell photodetector behind the focus. The relative phase of the zero-crossings of the AC-coupled bicell signals is detected electronically to obtain the voltage vs. focus discriminant. Two electronic detection algorithms are described and discriminants obtained with than in a typical implementation of the technique are presented. Also described are two techniques that have been used to compensate the detector signals for rapid fluctuations in the source intensity, if the fluctuations are rapid enough to interfere with the phase detection process. This focus sensing technique is sensitive primarily to focus, but some sensitivity to certain other wave-front ahprrations also exists. These sensitivities have been computed for two particular cases, the resolved spot source (with a geometrical analysis) and the unresolved point source (with a diffraction analysis). These results are tabulated for the Zernike aberrations up to m = n = 8.

A quantitative shadow method was developed and tested by measuring the one-dimensional refractive index distribution of a polished slab of gradient index glass. Tests made on the known glass sample showed that a one-dimensional index distribution can be measured by shadowgraphy to better than one percent accuracy. The method uses simple optics and can easily be automated to perform rapid measurements. Extension of the shadow method to more general distributions requires making many traverses of the refractive index distribution with a narrow sheet of light.