Shack-Hartmann Test Research Articles

Testing concave optical surface by Shack–Hartmann test using microholes

We present experimental results for testing concave optical surfaces by the Shack–Hartmann (S–H) test, where a set of microholes is used instead of the array of lenses employed in the original (S–H) plate.

Zonal processing of Hartmann or Shack-Hartmann patterns.

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests, we measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. In this paper, we describe a proposed new zonal procedure. This method finds a different analytical expression for each square cell formed by four sampling points in the pupil of the system. In this manner, a full single analytical expression for the wavefront is not obtained. The advantage is that small localized errors that cannot be adjusted by a single polynomial function can be represented with this method. A second advantage is that the analytical function for each cell is obtained in an exact manner, without the errors in a trapezoidal integration.

Least-squares fitting of Hartmann or Shack-Hartmann data with a circular array of sampling points.

A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigmatism by means of measurements of the transverse aberrations using a Hartmann or Shack-Hartmann test is described. The sampling points are distributed in a ring centered on the pupil of the optical system. The properties and characteristics of rings with three, four, five, six, or more sampling points are analyzed with more detail and better mathematical analysis than in previous publications.

Modal processing of Hartmann and Shack-Hartmann patterns by means of a least squares fitting of the transverse aberrations.

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests measure wavefront slopes, which are equivalent to ray transverse aberrations. Numerous integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. Frequently, a least squares fit of the transverse aberrations in the x direction and a least squares fit of the transverse aberrations in the y direction is performed to obtain the wavefront. In this work, we briefly describe a modal method to integrate Hartmann and Shack-Hartmann patterns by means of a single least squares fit of the transverse aberrations simultaneously instead of the traditional x-y separate method. The proposed method uses monomial calculation instead of using Zernike polynomials, to simplify numerical calculations. Later, a method is proposed to convert from monomials to Zernike polynomials. An important obtained result is that if polar coordinates are used, angular transverse aberrations are not actually needed to obtain all wavefront coefficients.

Shack–Hartmann mask/pupil registration algorithm for wavefront sensing in segmented mirror telescopes

Shack-Hartmann wavefront sensing in general requires careful registration of the reimaged telescope primary mirror to the Shack-Hartmann mask or lenslet array. The registration requirements are particularly demanding for applications in which segmented mirrors are phased using a physical optics generalization of the Shack-Hartmann test. In such cases the registration tolerances are less than 0.1% of the diameter of the primary mirror. We present a pupil registration algorithm suitable for such high accuracy applications that is based on the one used successfully for phasing the segments of the Keck telescopes. The pupil is aligned in four degrees of freedom (translations, rotation, and magnification) by balancing the intensities of subimages formed by small subapertures that straddle the periphery of the mirror. We describe the algorithm in general terms and then in the specific context of two very different geometries: the 492 segment Thirty Meter Telescope, and the seven "segment" Giant Magellan Telescope. Through detailed simulations we explore the accuracy of the algorithm and its sensitivity to such effects as cross talk, noise/counting statistics, atmospheric scintillation, and segment reflectivity variations.

Analysis of the common characteristics of the Hartmann, Ronchi, and Shack–Hartmann tests

An overview of the settings of the planes for the filters and observed patterns in the Hartmann and Ronchi tests is presented. Also a new set of filters for both test were developed. In a similar way, it is easy to extend this analysis to the Shack–Hartmann test, and to propose a new Null Shack–Hartmann filter.

Fresnel phasing of segmented mirror telescopes

Shack-Hartmann (S-H) phasing of segmented telescopes is based upon a physical optics generalization of the geometrical optics Shack-Hartmann test, in which each S-H lenslet straddles an intersegment edge. For the extremely large segmented telescopes currently in the design stages, one is led naturally to very large pupil demagnifications for the S-H phasing cameras. This in turn implies rather small Fresnel numbers F for the lenslets; the nominal design for the Thirty Meter Telescope calls for F=0.6. For such small Fresnel numbers, it may be possible to eliminate the lenslets entirely, replacing them with a simple mask containing a sparse array of clear subapertures and thereby also eliminating a number of manufacturing problems and experimental complications associated with lenslets. We present laboratory results that demonstrate the validity of this approach.

Hyperspectral Shack–Hartmann test

A hyperspectral Shack-Hartmann test bed has been developed to characterize the performance of miniature optics across a wide spectral range, a necessary first step in developing broadband achromatized all-polymer endomicroscopes. The Shack-Hartmann test bed was used to measure the chromatic focal shift (CFS) of a glass singlet lens and a glass achromatic lens, i.e., lenses representing the extrema of CFS magnitude in polymer elements to be found in endomicroscope systems. The lenses were tested from 500 to 700 nm in 5 and 10 nm steps, respectively. In both cases, we found close agreement between test results obtained from a ZEMAX model of the test bed and test lens and those obtained by experiment (maximum error of 12 μm for the singlet lens and 5 μm for the achromatic triplet lens). Future applications of the hyperspectral Shack-Hartmann test include measurements of aberrations as a function of wavelength, characterization of manufactured plastic endomicroscope elements and systems, and reverse optimization.

Generalized wave-front reconstruction algorithm applied in a Shack–Hartmann test

A generalized numerical wave-front reconstruction method is proposed that is suitable for diversified irregular pupil shapes of optical systems to be measured. That is, to make a generalized and regular normal equation set, the test domain is extended to a regular square shape. The compatibility of this method is discussed in detail, and efficient algorithms (such as the Cholesky method) for solving this normal equation set are given. In addition, the authors give strict analyses of not only the error propagation in the wave-front estimate but also of the discretization errors of this domain extension algorithm. Finally, some application examples are given to demonstrate this algorithm.

Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm

To achieve its full diffraction limit in the infrared, the primary mirror of the Keck telescope (now telescopes) must be properly phased: The steps or piston errors between the individual mirror segments must be reduced to less than 100 nm. We accomplish this with a wave optics variation of the Shack-Hartmann test, in which the signal is not the centroid but rather the degree of coherence of the individual subimages. Using filters with a variety of coherence lengths, we can capture segments with initial piston errors as large as +/-30 microm and reduce these to 30 nm--a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of approximately 75 nm.