Automated phase-measuring profilometry：a phase mapping approach

1.
Introduction
across the object is linearly related to the object height.
The images were recorded on a 128
X
Noncontact automated optical methods have been
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Automated phase-measuring profilometry: approach
V. Srinivasan, H. C. Liu, and Maurice Halioua
a phase mapping
When a sinusoidal grating is projected on either a reference plane or a diffuse object to be measured, every point along a line normal to the grating lines, on the reference plane as well as the object, can be character-
Ill.
REFERENCE PnANE
C B A
Experiment and Results
For experimental measurements, sinusoidal gratings wave grating pattern. A conventional slide projector was modified in order to operate with a grating slide, mounted on a stepper motor-driven translation stage. The period of the projected grating measured on the reference plane, close to the optical axis of projection,, was -15 mm. Deformed grating images were recorded on a 128 X 128 photodiode array detector interfaced to an LSI 11/23 computer for data acquisition and processing. Phase measurement was by a three discrete phase shift implementation of Eq. (3). The results of a calibration experiment, in which a cylindrical test object which had been measured by a mechanical contact profilometer, are shown in Fig. 2. The line profile was generated by the optical method and the X marks indicate measurements made by a manual contact profilometer. Almost perfect agreement (better than 1%)was observed, except in the regions with steep slopes where mechanical contact methods are not very reliable. A more general type of diffuse object-a mannequin face-was measured. Figure 3 shows the deforment of an image
sensing array. The intensity variation along x on the reference plane can be described by the equation
widely recognized as having potential advantages in the
128 photodiode
measurement to various diffuse objects ranging from machine parts of the human body. Several optical vision systems capable of monitoring critical in-plane dimensions, such as hole diameters on manufactured components, are available. For depth or profilometric measurements, methods requiring the projection of known grid patterns on the object to be measured and analyzing the deformed image of the grid have been studied, 1-8 and most of the current research is aimed at developing high speed on line systems.4-8 Noting that, in the case of projection of a sinusoidal grating, the mathematical representation of the deformed grating intensity distribution is similar to that observed in two-beam interferometry, we recently
15 January 1985 / Vol. 24, No. 2 / APPLIED OPTICS 185
.DETECFOR ARRAY
Ilomm
z
1.
Fig. 2.
Profile of a cylindrical test object:
comparison between
optical (line) and contact (X) measurements.
II. Theory
by a phase measuring technique, analogousto that used in interferometry. Results were obtained by illuminating the object with collimated laser light, passing through a polarization interferometer, and generating a sinusoidal intensity distribution. It was shown that, in such a system, the difference in phase between the intensity variation across a reference plane and that
where a (x,y) is the background or dc light level and b(xy) is the fringe contrast. The phase 0 is a nonlinear function of x because of the divergent nature of the image forming rays. With respect to a reference point such as 0, every point on the reference plane is characterized by a unique phase value. For example, the point C, observed by the detector D, of the array, has
proposed 8 an analysis of such a deformed grating image
array and processed by a microcomputer. To make the system more practical and capable of handling large objects, we replaced collimated laser illumination by the projected image of a white light illuminated sinusoidal transmission grating. The analysis, because of the divergent nature of the illumination
and because the optical axes of the projection and imaging systems are not necessarily parallel, is more
complicated and requires a different approach. To deal
The optical geometry of the projection and recording
systems is shown in Fig. 1. P1 and P 2 are the centers of
the entrance and exit pupils of the projection optics. I, and I2 are the centers of the exit and entrance pupils of the imaging optics. G is a grating with pitch po and a sinusoidal intensity transmission. D, is a photodiode
IR = a(xy) + b(xy) cosq(x), (1)
The authors are with New York Institute of Technology, Center for Optics, Lasers, and Holography, and NYCOM, Old Westbury, New York 11568. Received 20 June 1984. 0003-6935/85/020185-04$02.00/0. © 1985 Optical Society of America.
ized by a unique phase value. By measuring this phase accurately using phase modulation methods and by determining points on the reference plane and the object having identical phases, it is shown that the object height can be computed. A working system requires a projector, a translatable sinusoidal grating, and a detector array interfaced to a microcomputer. Results of measurements on diffuse test objects are described and errors are analyzed.
with such a generalized geometry, here we describe a new phase mapping algorithm. Results from measurements of a cylindrical test object and a mannequin head are given, together with an error and performance estimation.