David J. Lee

Cramér–Rao analysis of phase-diverse wave-front sensing

Phase-diverse wave-front sensing (PDWFS) is a methodology for estimating aberration coefficients from multiple incoherent images whose pupil phases differ from one another in a known manner. With the use of previous work by other authors, the Cramer–Rao lower-bound (CRLB) expression for the phase diversity aberration estimation problem is developed and is generalized slightly to allow for multiple phase-diverse images, various beam-splitting configurations, and imaging of known extended objects. The CRLB for a given problem depends implicitly on the true underlying value of the aberration being estimated. Therefore we use numerical evaluation and Monte Carlo analysis of the PDWFS CRLB expressions. The numerical evaluation is performed on an ensemble of aberration phase screens while simulating a number of different imaging configurations. We demonstrate the use of average CRLB values as figures of merit in comparing these various PDWFS configurations. For simulated point-source imaging we quantify the effects of varying the amounts and the types of diversity phase and briefly address the issue of the number of diversity images. Our results show that there is a diversity defocus configuration that is optimal in a Cramer–Rao sense for estimating certain aberrations. We also show that PDWFS Cramer–Rao squared-error values can be orders of magnitude higher for imaging of an extended target object than those from a point-source target.

Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing

Because of mechanical aspects of fabrication, launch, and operational environment, space telescope optics can suffer from unforeseen aberrations, detracting from their intended diffraction-limited performance goals. We give the results of simulation studies designed to explore how wave-front aberration information for such near-diffraction-limited telescopes can be estimated through a regularized, low-pass filtered version of the Gonsalves (least-squares) phase-diversity technique. We numerically simulate models of both monolithic and segmented space telescope mirrors; the segmented case is a simplified model of the proposed next generation space telescope. The simulation results quantify the accuracy of phase diversity as a wave-front sensing (WFS) technique in estimating the pupil phase map. The pupil phase is estimated from pairs of conventional and out-of-focus photon-limited point-source images. Image photon statistics are simulated for three different average light levels. Simulation results give an indication of the minimum light level required for reliable estimation of a large number of aberration parameters under the least-squares paradigm. For weak aberrations that average a 0.10lambda pupil rms, the average WFS estimation errors obtained here range from a worst case of 0.057lambda pupil rms to a best case of only 0.002lambda pupil rms, depending on the light level as well as on the types and degrees of freedom of the aberrations present.

Supersampling multiframe blind deconvolution resolution enhancement of adaptive optics compensated imagery of low earth orbit satellites

We describe a postprocessing methodology for reconstructing undersampled image sequences with randomly varying blur that can provide image enhancement beyond the sampling resolution of the sensor. This method is demonstrated on simulated imagery and on adaptive- optics-(AO)-compensated imagery taken by the Starfire Optical Range 3.5-m telescope that has been artificially undersampled. Also shown are the results of multiframe blind deconvolution of some of the highest quality optical imagery of low earth orbit satellites collected with a ground- based telescope to date. The algorithm used is a generalization of multiframe blind deconvolution techniques that include a representation of spatial sampling by the focal plane array elements based on a forward stochastic model. This generalization enables the random shifts and shape of the AO-compensated point spread function (PSF) to be used to partially eliminate the aliasing effects associated with sub-Nyquist sampling of the image by the focal plane array. The method could be used to reduce resolution loss that occurs when imaging in wide-field-of-view (FOV) modes.

Starfire Optical Range 3.5-m telescope adaptive optical system

A 941 channel, 1500 Hertz frame rate adaptive optical (AO) system has been installed and tested in the coude path of the 3.5m telescope at the USAF Research Laboratory Starfire Optical Range. This paper describes the design and measured performance of the principal components comprising this system and present sample results from the first closed-loop test of the system on stars and an artificial source simulator.

Fiber developments at the Anglo-Australian Observatory for SPIRAL and AUSTRALIS

In this paper we discuss some of the recent developments with optical fibers at the Anglo-Australian Observatory. Firstly we will describe the upgrade to the SPIRAL integral field spectrograph for the Anglo-Australian Telescope. SPIRAL-B uses a crossed cylindrical microlens array to feed 512 optical fibers at F/5.5 providing a field of view of 22 by 11 arcseconds with 0.7 arcsecond spatial sampling. The performance of the fiber bundle, microlens array, and construction techniques will be described. We will also discus the development of prototype optical fiber switchyard as part of the AUSTRALIS concept study. The switchyard provides an optical bread in the fiber, between the telescope and spectrograph, which allows coupling between fibers of different diameters and focal rations. A dichroic can also be incorporated into the switchyard to allow both optical and IR spectrographs to be fed simultaneously. Switchyards therefore provide much greater observing flexibility by increasing the number of possible instrument configurations. We will briefly discuss the merits of fiber switchyards and present the results of FRD and transmission test performed in the laboratory.

Characterization of microlens arrays for integral field spectroscopy

One of the most exciting operational modes of the new generation of 8-m class telescopes will be integral field spectroscopy. Many of the current designs of integral field units use microlens arrays as a way of sampling the focal plane of the telescope. Integral field spectroscopy places demanding requirements on the optical quality of the microlens arrays. In this paper we describe these requirements and report on an extensive series of optical tests to characterize microlens arrays in the laboratory. The tests were carried out on prototype microlens arrays intended for use in various Durham instrument projects. The lenses tested had excellent positional accuracy and consistency of focal length. However detailed measurements of the point spread function showed a core with good image quality but with a background level of diffuse scattered light. This scattered light causes a throughput loss in the instrument of around approximately 20%. This result was verified for the Spectroscopic Multimode InfraRed Fiber System (SMIRFS) integral field unit by absolute throughput tests carried out during commissioning of the instrument at the United Kingdom Infrared Telescope.

Supersampling multiframe blind deconvolution resolution enhancement of adaptive-optics-compensated imagery of LEO satellites

A post-processing methodology for reconstructing undersampled image sequences with randomly varying blur is described which can provide image enhancement beyond the sampling resolution of the sensor. This method is demonstrated on simulated imagery and on adaptive optics compensated imagery taken by the Starfire Optical Range 3.5 meter telescope that has been artificially undersampled. Also shown are the results of multiframe blind deconvolution of some of the highest quality optical imagery of low earth orbit satellites collected with a ground based telescope to date. The algorithm used is a generalization of multiframe blind deconvolution techniques which includes a representation of spatial sampling by the focal plane array elements in the forward stochastic model of the imaging system. This generalization enables the random shifts and shape of the adaptive compensated PSF to be used to partially eliminate the aliasing effects associated with sub- Nyquist sampling of the image by the focal plane array. The method could be used to reduce resolution loss which occurs when imaging in wide FOV modes.

Characterization of cooled infrared fibers for the Gemini IRMOS

Recently integral field spectroscopy has become a band-wagon among the optical astronomical community and most of the 8m class telescopes plan to offer this as part of their instrumentation package. The possibility of expanding integral field spectrsopcy into the near IR opens exciting new possibilities for the study of a variety of astronomical objects.

Analysis of atmospheric turbulence measurements obtained with the Starfire Optical Range 3.5-m telescope adaptive optical system

The adaptive optical system for the Starfire Optical Range 3.5-meter telescope includes a SHack-Hartmann wavefront sensor (WFS) with 30 by 30 subapertures and a continuous facesheet deformable mirror (DM) with 31 by 31 actuators within the telescope aperture. Time histories of turbulence- induced phase distortions have been estimated from WFS gradient measurements and DM actuator commands acquired simulators with the adaptive optics loop closed. The statistics of these phase distortion profiles have been characterized in terms of spatial structure functions, Zernike coefficient statistics, and temporal power spectral densities. The results obtained are in good agreement with predictions based upon Kolmogorov theory.

Single-input/single-output analysis of latency and quadrant detector saturation in adaptive optical systems

Feedback control theory offers several useful tools for analysis of adaptive optics systems. The basic tools of single-input-single-output analysis are applied to design first order and optimal filters for a specific loop bandwidth or gain margin as a function of latency and sample rate. Optimizing filter loop band-width as a function of temporal disturbance and noise statistics is addressed with respect to the internal model principles. Latency, due to camera readout and processing time, is shown to be the primary design driver for optical AO system performance. The effects of wavefront sensor saturation are discussed and simulation and experimental results are presented.