Binary arrays with perfect odd-periodic autocorrelation

Lüke, Hans Dieter; Busboom, Axel

doi:10.1364/ao.36.006612

Cited by 18 publications

(8 citation statements)

References 23 publications

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“…Discussion of the choice of algorithm for placing the holes has concentrated on designs in which the (cyclic) autocorrelation function of the pattern, sampled at shifts corresponding to a whole number of cells of the grid, is bivalued with a central peak and flat wings. An extensive literature [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] exists on arrays which have this property, which are usually termed 'Uniformly Redundant Arrays' (URAs). For URA-based masks, in certain well defined circumstances, cross-correlation of the recorded data with an array which corresponds to the mask pattern (with a scaling and offset applied) leads to images with a point source response function (PSF) having a central peak and perfectly flat side-lobes.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity of coded mask telescopes

Skinner

2008

Appl. Opt.

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Simple formulae are often used to estimate the sensitivity of coded mask X-ray or gamma-ray telescopes, but these are strictly only applicable if a number of basic assumptions are met. Complications arise, for example, if a grid structure is used to support the mask elements, if the detector spatial resolution is not good enough to completely resolve all the detail in the shadow of the mask or if any of a number of other simplifying conditions are not fulfilled. We derive more general expressions for the Poisson-noise-limited sensitivity of astronomical telescopes using the coded mask technique, noting explicitly in what circumstances they are applicable. The emphasis is on using nomenclature and techniques that result in simple and revealing results. Where no convenient expression is available a procedure is given which allows the calculation of the sensitivity. We consider certain aspects of the optimization of the design of a coded mask telescope and show that when the detector spatial resolution and the mask to detector separation are fixed, the best source location accuracy is obtained when the mask elements are equal in size to the detector pixels.

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Section: Introductionmentioning

confidence: 99%

Sensitivity of coded mask telescopes

Skinner

2008

Appl. Opt.

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“…It also provides a measure of the system MTF averaged over the entire extent of the aperture, rather than just in a very localized region around the height discontinuity of the single step artifact. 12,13 Particular methods for generation of maximum-length pseudo-random sequences [14][15][16] Similar to the requirement for maximum duty cycle of a pseudo-random chopper, the BPR grating has to be generated with a maximum filling factor for an improved signal-to-noise ratio of the PSD spectra of the test surface. The mathematical term for such a sequence is "maximumlength pseudo-random sequence" (MLPRS).…”

Section: Binary Pseudo-random Grating Propertiesmentioning

confidence: 99%

Binary pseudorandom grating standard for calibration of surface profilometers

2008

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We suggest and describe the use of a binary pseudo-random (BPR) grating as a standard test surface for measurement of the modulation transfer function (MTF) of interferometric microscopes. Knowledge of the MTF of a microscope is absolutely necessary to convert the measured height distribution of a surface undergoing metrology into an accurate power spectral density (PSD) distribution. For an 'ideal' microscope with an MTF function independent of spatial frequency out to the Nyquist frequency of the detector array with zero response at higher spatial frequencies, a BPR grating would produce a flat 1D PSD spectrum, independent of spatial frequency. For a 'real' instrument, the MTF is found as the square root of the ratio of the PSD spectrum measured with the BPR grating to the 'ideal', spatial frequency independent, PSD spectrum. We present the results from a measurement of the MTF of Micromap TM -570 interferometric microscope demonstrating a high efficiency for the calibration method.

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“…Particular methods for generation of maximum-length pseudorandom sequences [12][13][14] were developed in connection with the use of pseudorandom chopping of a beam in time-of-flight experiments. [15][16][17] The sequences are mathematically represented with 1's, which denote an open chopper slot, and 0's, which denote a closed chopper slot.…”

Section: Mathematical Background Of Binary Pseudo-random Grating Stanmentioning

confidence: 99%

Binary pseudo-random grating as a standard test surface for measurement of modulation transfer function of interferometric microscopes

Yashchuk

McKinney²,

Takacs

2007

Advances in Metrology for X-Ray and EUV Optics II

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TitleBinary pseudo-random grating as a standard test surface for measurement of modulation transfer function of interferometric microscopes ABSTRACTThe task of designing high performance X-ray optical systems requires the development of sophisticated X-ray scattering calculations based on rigorous information about the optics. One of the most insightful approaches to these calculations is based on the power spectral density (PSD) distribution of the surface height. The major problem of measurement of a PSD distribution with an interferometric and/or atomic force microscope arises due to the unknown Modulation Transfer Function (MTF) of the instruments. The MTF characterizes the perturbation of the PSD distribution at higher spatial frequencies. Here, we describe a new method and dedicated test surfaces for calibration of the MTF of a microscope. The method is based on use of a specially designed Binary Pseudo-random (BPR) grating. Comparison of a theoretically calculated PSD spectrum of a BPR grating with a spectrum measured with the grating provides the desired calibration of the instrumental MTF. The theoretical background of the method, as well as results of experimental investigations are presented.

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Binary arrays with perfect odd-periodic autocorrelation

Cited by 18 publications

References 23 publications

Sensitivity of coded mask telescopes

Sensitivity of coded mask telescopes

Binary pseudorandom grating standard for calibration of surface profilometers

Binary pseudo-random grating as a standard test surface for measurement of modulation transfer function of interferometric microscopes

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