Ronchi Grating Research Articles

Surface measurement based on chessboard-shaped 2-D Ronchi grating method

A method for surface profile measurement using a chessboard-shaped 2-D Ronchi grating is proposed. The gradients in two orthogonal directions of the measured surface can be obtained simultaneously using a chessboard-shaped 2-D Ronchi grating, so that it is possible to reconstruct the surface profile by means of only one Ronchigram with high accuracy. The measuring principle and the design of the chessboard-shaped 2-D Ronchi grating are described. Measurements of both stationary and varying surfaces using an instrument constructed on the basis of the method were conducted with satisfactory results.

Simultaneous and real-time measurement of slope and curvature fringes in thin structures using shearing interferometery

A real-time lateral shearing interferometry that uses a pair of Ronchi gratings to perform wavefront shearing operations is described for measuring slope and curvature fringes simultaneously in thin structures. It involves simultaneous imaging of diffracted wavefronts using Fourier filtering. Two sets of fringe patterns, one representing slopes and the other curvatures, occur simultaneously at spatially distinct locations on the image plane, thereby eliminating the need for additional postprocessing of the recordings. In this work, the principles involved in the measurement of slopes and curvatures using this technique are explained. The method is then demonstrated on thin structures subjected to well-defined loading conditions, such as a clamped circular silicon wafer subjected to central displacement. Measurements have been successfully compared with analytical solutions.

Novel method for testing the long focal length lens of large aperture

In this paper, we present a novel method for testing the long focal length lens of large aperture, which is realized by calculating the angle of moiré fringe formed by Talbot image of two Ronchi gratings. A scanning method was developed to measure the focal length with the collimated lights projected on the different aperture position of the lens. Experiment data demonstrates that this method can be applied to the real-time long focal length measurement with high accuracy.

Flatness measurement by a grazing Ronchi test

The Ronchi test with a LCD amplitude sinusoidal grating is used for testing nominally flat surfaces. We prove that it is possible to measure flat surfaces without using a reference element by modifying the common optical Ronchi set up. The Ronchi rulings are computer generated and displayed on the LCD. By displaying various phase-shifted rulings and capturing the corresponding images, the phase is obtained with the conventional phase-shifting algorithms. Theoretical and experimental results are shown.

Real-Time Shape Measurement by Integrated Phase-Shifting Method Using Ronchi Grating

Phase-shifting methods for analyzing phases of a grating projected onto an object are useful to measure the shape of the object accurately. Conventional phase-shifting methods usually uses three or four cosinusoidal phase-shifted images. The grating images are recorded with stopping phase-shifting so that the brightness does not change during the exposure time of the camera. The stopping procedure, however, obstructs speed up of the measurement system and it is difficult to produce a grating film which has an accurate cosinusoidal brightness distribution. In this paper, an integrated phase-shifting method (IPSM) using a Ronchi grating is proposed. This method is suitable for real-time phase analysis. The theory and an application for shape measurement of a deformed tire are shown.

Displacement measurement using the Talbot effect with a Ronchi grating

In this study the Talbot effect with a Ronchi grating is applied to measurement of shift. It is shown that by using a measurement procedure based on the Fourier transform a cosine grating can be replaced by a Ronchi grating. Two different methods for data reduction and some experimental results are given.

Automatic wavefront measurement technique using a computer display and a charge-coupled device camera

A simple and fully automated technique for wavefront measurement is presented. This technique is based on the use of a computer display (for example, a CRT or a thin film transistor (TFT) monitor) to generate intensity-modulated patterns from which images are taken by a CCD camera. When a phase object is located between the display and the camera, the intensity patterns are distorted. By measuring this distortion, the gradients of the phase change caused by the object can be obtained. To simplify the data analysis it is practical to display on the monitor a grating with a sinusoidal intensity profile, which enables the use of standard fringe pattern analysis techniques. We use phase-shifting and temporal phase-unwrapping techniques. The use of a computer display for fringe (or grating) generation leads to the possibility of adjusting the sensibility of the measurement in function of the phase variation of the object to test and avoiding the problems of having a fixed grating period (as in the case of Ronchi rulings or printed gratings) or using mechanical parts to change them. Experimental measurements of two different ophthalmic lenses with local distributions of focal lengths prove the versatility of this method for optical testing. The method is simple, flexible, and low cost, yet it yields a remarkably high SNR. Compared with other techniques such as interferometry and moire deflectometry, the setup is cheaper and far easier to align.

接触時の等高線を表示する触覚センサー

A tactile sensor using moiretopography is developed. The sensor is composed of a Ronchi grating, a gel sheet, light scatterers, a light source and an ITV camera. Using the sensor, contour lines of an object with which the sensor touches were extracted and shape of an object in a visco-elastic object was found.

Ultraresolution in optical imaging using spatiotemporal scanning.

Spatial information exceeding the passband of an imaging system can be captured by using the optics to generate a spatiotemporal multiple beam interference pattern that is scanned over the object, rather than using it to image the object directly. The modulation of the higher temporal harmonics of the signal resulting from collecting the scattered light represents a mapping in the time domain of higher spatial harmonics of the data. Upon reconstruction, the additional temporal degrees of freedom are mapped back in the spatial domain where they represent spatial frequencies exceeding the passband of the optics. The spatial resolution is thus not limited by the spatial passband, but rather by the temporal bandwidth of the detection system. Due to hardware limitations, experimental demonstration is provided only for a one-dimensional scan of Ronchi gratings with 50 and 200 lines per inch.

Space integrating joint transform correlator using a moving grating

A new one-step joint transform correlator (JTC) is presented, in which the joint transform of the images to be correlated is filtered by a moving Ronchi ruling. An alternative JTC architecture without moving parts using two Ronchi rulings is also suggested. A lens produces the spatial integral of the product of the joint transform image and the trans- mission factor of the Ronchi ruling, and a single element detector is used to capture the integral. The amplitude of the light modulation on the detector gives the cross-correlation function of the input images at coor- dinates (0,0) without major processing. Therefore, in principle this tech- nique significantly reduces the time required to evaluate the cross- correlation function, compared to that for usual JTCs. Experimental validation of the proposed one-step architecture is presented. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)01807-3)

Profile measurement taken with liquid-crystal gratings

Profile measurement taken with liquid-crystal gratings and a phase-shifting technique is proposed, and its effectiveness is verified by experiment. The surface profile is obtained by measurement of the phase distributions of the sinusoidal gratings deformed by an object's surface. The liquid-crystal grating gives an accurate phase shift, an arbitrary projection pitch, and a constant surface brightness compared with conventional gratings such as a laser interference fringe grating and a Ronchi grating. Therefore a flexible measuring system may be developed with it. Two gratings with different pitches are used to measure an object with large steps. A two-color projection system can be used to produce such gratings simultaneously. Locally varying reflectivity on a surface can also be compensated by adjustment of the color component of the projected grating with a liquid-crystal grating. Thus the contrast in the projected grating can be made uniform, and a good profile measurement can be accomplished.

Dynamic coherent focus OCT with depth-independent transversal resolution

We present a new OCT technique which renders the transversal resolution depth independent. This is achieved by an optical setup which shifts the focus of the beam illuminating the object through the object depth without changing the path length in the corresponding interferometer arm. Therefore, the coherence gate remains at the beam focus without any readjustment of the reference arm. Depth resolution was tested with the help of microscopy cover-plates and transversal resolution was tested with the help of Ronchi rulings. Resolution was 100 lines mm−1 over an object depth of 430 μm. For a first demonstration of the properties of this dynamic coherent focus scheme in a biologic system a section of a human cornea was used. We expect that this technique can further be improved to obtain transversal resolution down to the 1-μm range

Technique for diagnosing x-ray laser beam quality by use of the moiré signal

We present what we believe is a novel technique based on the moiré effect for fully diagnosing the beam quality of an x-ray laser. Using Fresnel diffraction theory, we investigated the intensity profile of the moiré pattern when a general paraxial beam illuminates a pair of Ronchi gratings in the quasi-far field. Two formulas were derived to determine the beam quality factor M2 and the effective radius of curvature Re from the moiré pattern. On the basis of the results, the far-field divergence, the waist location, and the radius can be calculated further. Finally, we verified the approach by use of numerical simulation.

Highly stable differential phase optical interferometer using rotating Ronchi gratings

We describe a dual-beam differential phase interferometer that performs direct phase measurement by using a rotating Ronchi grating filter. Two laser beams derived from a single source are focused onto the sample surface. The reflected light will retrace the same path and intersect at the back focus of the objective lens. Interference between the reflected rays will therefore produce intensity fringes with their spatial location governed primarily by the differential optical phase of the probes. When the fringes are projected onto a rotating grating filter with identical periodicity, the transmitted optical signal becomes an oscillating signal from which the optical phase can be measured by standard phase-sensitive techniques. This approach has the advantages of simple system configuration, effective isolation from environmental disturbance, and low-frequency operation, which permit the use of high impedance electronics with shot-noise-limited performance at low laser power.

Polarization-sensitive readout of self-images

When a Ronchi grating is stored as modulation of birefringence, it can be replicated (Talbot effect) if read out with coherent light. This is obtained by writing an incoherently projected grating in a photorefractive BSO crystal. Then, it is read out by collimated polarized laser light, which is outside of the crystal spectral sensitivity range. The ellipticity of the readout light exiting the crystal is determined according to the local birefringence. By rotating an analyzer the contrast of the free propagation replicated grating is controlled. Experimental results are presented.

Amplitude checker grating from one-dimensional Ronchi grating and its application to array generation

The Ronchi grating is well known for its many applications in areas such as spectroscopy, grating interferometry, and Talbot interferometry. On the other hand, the checker grating has attracted very little attention. A checker grating also self-images at equidistant planes; the separation between these planes is a quarter of the Talbot distance of a Ronchi grating of the same period. To understand this and several other features, a transition from Ronchi grating (a one-dimensional grating) to checker grating (a two-dimensional grating) has been both theoretically and experimentally studied and results are presented. Because the checker grating self-images closer to the grating and its transmittance is higher than that of a Ronchi grating, the use of its self-image planes for array generation is also emphasized.

Spatial frequency filtering in holographic image reconstruction

We show that reconstructing a hologram by its object beam leads to spatial filtering, namely, to the suppression of spatial frequency components that are perpendicular to the plane of the recording beams. We conduct experiments by rotating the transparencies of Ronchi gratings and crossed gratings and measuring the corresponding diffraction efficiencies. Good agreement is found with a theory based on image reconstruction with a beam that does not quite satisfy the Bragg condition.

3D Reconstruction of Large-Depth Objects Using Fresnel Diffraction of a Ronchi Grating and Simultaneous Recording of Reference and Object Fringes

We propose an active triangulation based range-finding system that, besides its simplicity, has two advantages over similar existing systems. First, the system can acquire range data for large-depth objects since it generates an illumination pattern with large-depth of focus using Fresnel diffraction from a Ronchi grating projected over the entire object surface. Secondly, the system does not need preliminary recording of reference fringes since it displays simultaneously, on a single image, both reference and object deformed fringes. This system offers other properties: it is mechanically simple, uses everyday optical components, is low cost, can be operated via a PC and uses relatively simple image analysis software. Three dimensional reconstructions are illustrated for various objects having 10 cm maximum depth variations. The depth accuracy (typically 0.5 mm for an object located at 350 mm from the camera) is comparable with other systems, but a certain compromise has to be accepted in acquisition time (typically 1 minute). This system can find applications in research laboratories as a tool to provide range data with relatively good depth accuracy.

Direct-phase detection of modulated Ronchi rulings using a phase-locked loop

A recently developed technique for fringe analysis based on a digital phase-locked loop is applied to detect the ray aberration of modulated Ronchi rulings. The Ronchi ruling is placed outside the caus- tic, and the shadow of the ruling is imaged directly into a two-dimensional CCD video array for further processing. The CCD array is placed at a

A light-emitting diode light standard for photo- and videomicroscopy.

A light calibration system consisting of a compact light-emitting diode (LED) source with feedback control of intensity is described. The source is positioned in the focal plane of the microscope objective and produces flat-field illumination of up to 31 microW. The source can be easily used to determine the performance of microscope optics and camera response. It can also be used as a standard light source for calibration of experimental systems. Selectable light intensities are produced by controlling the LED input power via a feedback circuit consisting of a photodiode that detects output light intensity. Spectral coverage extends between 550 and 670 nm using green, yellow and red LEDs mounted side by side, which are selected individually. The LED chips are encapsulated in plastic diffusers which homogenize the light, and a flat field of illumination is obtained through a thin 1-mm-diameter aperture positioned directly over each chip. Provision is made for insertion of Ronchi rulings over the aperture to enable measurements of contrast modulation in a uniform field. The light may be pulse-modulated to assess camera response times and the device can be synchronized with video frames. Narrow bandpass interference filters can be placed between the objective lens and the LED source to produce monochromatic light without affecting the spacing of controlled light intensities since emission spectra do not shift appreciably over the range of LED powers chosen in this design. Results of tests using controlled light intensity and uniform illumination are presented.