Experimental measurements of generalized grating images

Self-aligning CMOS photodetector sensor for application on an NDB-based optical encoder

In this work, a complementary metal-oxide-semiconductor (CMOS) photodetector specifically designed to be used in a non-diffracting-beam (NDB) optical encoder is introduced. The sensor is aimed to address the critical alignment of the NDB-based optical encoder head and consists of a hexagonal array of photodiodes that can be interconnected among themselves. The photodiodes' interconnection is configured by means of static random access memory (SRAM) cells and transistors that operate as configurable connection switches between each photodiode and three of its neighbor photodiodes. This feature of the photodetector makes it possible to implement a search algorithm in order to find the photodiode where the NDB center impinges and then configure the appropriate detectivity pattern centered on that photodiode. It is shown that the new sensor design remarkably simplifies the alignment of the system.

Performance of an optical encoder based on a nondiffractive beam implemented with a specific photodetection integrated circuit and a diffractive optical element

In this paper, we study the incremental signal produced by an optical encoder based on a nondiffractive beam (NDB). The NDB is generated by means of a diffractive optical element (DOE). The detection system is composed by an application specific integrated circuit (ASIC) sensor. The sensor consists of an array of eight concentric annular photodiodes, each one provided with a programmable gain amplifier. In this way, the system is able to synthesize a nonuniform detectivity. The contrast, amplitude, and harmonic content of the sinusoidal output signal are analyzed. The influence of the cross talk among the annular photodiodes is placed in evidence through the dependence of the signal contrast on the wavelength.

Relaxation of the Talbot condition in generalized grating imaging

We can form a grating image with two gratings having different pitches with an extended light source. It is called generalized grating imaging or the Talbot-Lau effect. When we want to obtain high contrast image with pure absorption gratings or pure phase gratings, the separation between the two gratings is restricted. This corresponds to the Talbot condition. In this paper, we propose to use a combination of absorption grating and phase grating to relax the separation restriction. The theory of generalized grating imaging is applied to the system with this kind of grating. Simulations are performed for calculating contrast variation and show that the proposed system practically relaxes the Talbot condition. An experiment verifies the result of the simulation.

Application of generalized grating imaging to pattern projection in three-dimensional profilometry

The theory of generalized grating imaging for a one-dimensional grating is applied to a pattern projection system in pattern projection profilometry. Contrast of the projected grating image is calculated under various conditions. The results help to determine the conditions suitable for obtaining high contrast grating images in a large space. Although the gratings required for the profilometry are hexagonal, the theory for two-dimensional gratings is prohibitively complex. Therefore, the projection system was designed using the one-dimensional theory. The projection system using two-dimensional hexagonal gratings was constructed and experiments were done with it. The result agrees approximately with the theoretical calculations for one-dimensional gratings. This suggests that the one-dimensional theory may be used for estimating the approximated behavior for hexagonal gratings for use in pattern projection profilometry. Some discussions are given for the application of the projection system for profiling the mannequin or human body.

White-light imaging analysis of bi-grating systems

Two gratings consist of an imaging system that forms a no-dispersion image of an object that is illuminated by white light. The process of double diffraction of the actual system is analyzed using the Fresnel diffraction approximation. One grating generates a number of spectral images of the diffraction orders of an object. The other grating combines one-order dispersive images into one and reconstructs a clear image. A bi-grating system in this case shows the same imaging capability as the lens, but its principle is completely different. An expression of the imaging rule is deduced that agrees well with experiments.

X-ray shearing interferometer and generalized grating imaging

X-ray shearing interferometers with three gratings are analyzed on the basis of generalized grating imaging theory. The result of this analysis is applied to an already proposed interferometer. The contrast of the imaging fringes in the interferometer is calculated quantitatively. It is also applied to explain the spatial resolution of the image.

Interpretation of generalized grating imaging: further analysis and numerical calculation

The generalized grating imaging based on the equations derived in a previous paper [J. Opt. Soc. Am. A25, 2244 (2008)] is described. There the fundamental order imaging was interpreted for gratings with real diffraction coefficients. Here the equations for higher-order imaging are derived and discussed for more general gratings with complex diffraction coefficients. Based on the derived equations the contrast of the grating image is calculated for two examples. A discussion of the effect of the spectrum width of the light source is made and applied to the examples.

Interpretation of generalized grating imaging

This paper describes generalized grating imaging with equations based on geometrical optics and wave optics. It shows that the equation derived by wave optics agrees well with the description by geometrical optics. The derived equation based on wave optics can be used to deduce and calculate the intensity distribution of the grating image.

Invariant grating pseudoimaging using polychromatic light and a finite extension source

The Talbot effect is a well studied phenomenon by which grating pseudoimages appear at certain periodic distances when monochromatic light is used. Recently, numerical simulations have shown a new phenomenon; when a polychromatic light beam is used in a double grating system, the intensity of the pseudoimages presents a transverse-profile that remains unaffected over a wide range of propagation distances. This effect can be used to increase the tolerances of gratings based optical devices, such as displacement measurement systems, interferometers, and spectrometers. The pseudoimages formation with a polychromatic and finite extension light source is analytically and experimentally demonstrated. Relatively simple analytical expressions for the intensity and the contrast allow us to predict when pseudoimages present a constant contrast and when they disappear. Furthermore, we experimentally obtain the pseudoimages using the proposed configuration, corroborating the theoretical predictions.

Collimation testing by use of the Lau effect coupled with moiré readout

We present an easy, simple, and inexpensive technique for checking the quality of the collimation of optical beams using the Lau effect combined with moiré readout. The experimental arrangement consists of a modified Lau-based interferometer in which a white-light incoherent source illuminates a set of two gratings. A collimating lens is placed between the two gratings such that the self-images of the second grating are formed. The third grating is positioned at one of the self-imaging planes forming moiré fringes. The type of the moiré fringe demonstrates the quality of collimation of the optical beam. The necessary theoretical background is presented and the results of our experimental investigation are reported. The technique can also be used for accurate determination of the focal length of a collimating lens using low-cost components.

Imaging with a rectangular phase grating applied to displacement metrology

We achieved displacement metrology with a high-amplitude signal by using a rectangular phase grating as the pupil in a grating imaging system. The imaging phenomenon with a pupil transmission grating that has a bilevel profile with a 50% duty ratio is discussed on the basis of the optical transfer function. By optimizing the imaging condition, we obtained high-contrast images with high light power under a magnified or demagnified imaging system. The amplitude of the signal in the displacement measurement was four times higher than that of the conventional grating imaging system with amplitude gratings.