Robert J. Noll

Bio: Robert J. Noll is an academic researcher from PerkinElmer. The author has contributed to research in topics: Light scattering & Surface roughness. The author has an hindex of 7, co-authored 12 publications receiving 2740 citations.

Zernike polynomials and atmospheric turbulence

Abstract: This paper discusses some general properties of Zernike polynomials, such as their Fourier transforms, integral representations, and derivatives. A Zernike representation of the Kolmogoroff spectrum of turbulence is given that provides a complete analytical description of the number of independent corrections required in a wave-front compensation system.

Effect of Mid- and High-Spatial Frequencies on Optical Performance

Abstract: In many of today's telescopes the effects of surface errors on image quality and scattered light are very important. The influence of optical fabrication surface errors on the performance of an optical system is discussed. The methods developed by Hopkins (1957) for aberration tolerancing and Barakat (1972) for random wavefront errors are extended to the examination of mid- and high-spatial frequency surface errors. The discussion covers a review of the basic concepts of image quality, an examination of manufacturing errors as a function of image quality performance, a demonstration of mirror scattering effects in relation to surface errors, and some comments on the nature of the correlation functions. Illustrative examples are included.

Mirror surface autocovariance functions and their associated visible scattering.

Abstract: Visible scattering is measured and compared with predictions based upon surface roughness measurements. The results indicate two scales of roughness, a short scale of the order of 1 microm and a long scale ranging from 30 to 150 microm. A study of the relative amount of scattering from the two scales shows that the short scale accounts for all the scattering for scattering angles larger than 3 degrees . Furthermore, the analysis demonstrates the importance of spatial frequency bandwidth limits in optical scattering and finish measurements for a particular class of highly polished mirror surfaces.

Reduction of diffraction of use of a Lyot stop

Abstract: The efficiency of a Lyot stop in reducing the effects of diffraction is analyzed for a Fourier optical system. The problem reduces to the evaluation of an integral whose integrand is the product of two Bessel functions of different order and argument. An analytic series solution is found for the reduction of diffracted light reaching the focal plane.

Optical communications using orbital angular momentum beams

Abstract: Orbital angular momentum (OAM), which describes the “phase twist” (helical phase pattern) of light beams, has recently gained interest due to its potential applications in many diverse areas. Particularly promising is the use of OAM for optical communications since: (i) coaxially propagating OAM beams with different azimuthal OAM states are mutually orthogonal, (ii) inter-beam crosstalk can be minimized, and (iii) the beams can be efficiently multiplexed and demultiplexed. As a result, multiple OAM states could be used as different carriers for multiplexing and transmitting multiple data streams, thereby potentially increasing the system capacity. In this paper, we review recent progress in OAM beam generation/detection, multiplexing/demultiplexing, and its potential applications in different scenarios including free-space optical communications, fiber-optic communications, and RF communications. Technical challenges and perspectives of OAM beams are also discussed.

Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods

Abstract: Two-dimensional (2D) phase unwrapping continues to find applications in a wide variety of scientific and engineering areas including optical and microwave interferometry, adaptive optics, compensated imaging, and synthetic-aperture-radar phase correction, and image processing. We have developed a robust method (not based on any path-following scheme) for unwrapping 2D phase principal values (in a least-squares sense) by using fast cosine transforms. If the 2D phase values are associated with a 2D weighting, the fast transforms can still be used in iterative methods for solving the weighted unwrapping problem. Weighted unwrapping can be used to isolate inconsistent regions (i.e., phase shear) in an elegant fashion.

Wave-front estimation from wave-front slope measurements

Abstract: The problem of wave-front estimation from wave-front slope measurements has been examined from a least-squares curve fitting model point of view. It is shown that the slope measurement sampling geometry influences the model selection for the phase estimation. Successive over-relaxation (SOR) is employed to numerically solve the exact zonal phase estimation problem. A new zonal phase gradient model is introduced and its error propagator, which relates the mean-square wave-front error to the noisy slope measurements, has been compared with two previously used models. A technique for the rapid extraction of phase aperture functions is presented. Error propagation properties for modal estimation are evaluated and compared with zonal estimation results.

Monochromatic aberrations of the human eye in a large population.

Abstract: From both a fundamental and a clinical point of view, it is necessary to know the distribution of the eye's aberrations in the normal population and to be able to describe them as efficiently as possible. We used a modified Hartmann-Shack wave-front sensor to measure the monochromatic wave aberration of both eyes for 109 normal human subjects across a 5.7-mm pupil. We analyzed the distribution of the eye's aberrations in the population and found that most Zernike modes are relatively uncorrelated with each other across the population. A principal components analysis was applied to our wave-aberration measurements with the resulting principal components providing only a slightly more compact description of the population data than Zernike modes. This indicates that Zernike modes are efficient basis functions for describing the eye's wave aberration. Even though there appears to be a random variation in the eye's aberrations from subject to subject, many aberrations in the left eye were found to be significantly correlated with their counterparts in the right eye.

Solar Image Restoration By Use Of Multi-frame Blind De-convolution With Multiple Objects And Phase Diversity

Abstract: An extension of Joint Phase Diverse Speckle image restoration is presented. Multiple realizations of multiple objects having known wavefront relations with each other can now be restored jointly. As the alignment of the imaging setup does not change, near-perfect alignment can be achieved between different objects, thus greatly reducing false signals in the determination of derived quantities, such as magnetograms, Dopplergrams, etc. The method was implemented in C++ as an image restoration server, to which worker clients can connect and disconnect randomly, so that a large number of CPUs can be used to speed up the restorations. We present a number of examples of applications of the restoration method to observations obtained with the Swedish 1-m Solar Telescope on La Palma.