Optical surface roughness detection method and apparatus

An optical method and apparatus for noncontacting inspection of a specimen to evaluate quantitatively its surface roughness characteristics are disclosed. The distribution of light scattered by a Gaussian rough surface illuminated with a laser beam is obtained with a transform and cylinder lens pair (for a one-dimensional light distribution), or by a transform lens alone (for a two-dimensional Gaussian light distribution) when no tooling marks, scratches, etc., would mar the surface and mask the measurement. Spatial frequency halfwidths of the optical Fourier transform spectrum of the scattered light are known to be linearly related to the planar surface roughness characteristics. Hence, with appropriate calibration, the measured light distribution halfwidths can be used to evaluate surface roughness. Measurements are not restricted to planar surfaces; curved specimen shapes can be employed with appropriate optical adjustments. Beam forming components can also be used to achieve similar surface roughness measurements on curved shapes, such as a conical mirror for use with cylindrical or tapered holes.

BACKGROUND OF THE INVENTION 
This invention relates to a noncontacting optical method and apparatus for 
evaluating the surface roughness characteristics of a specimen. More 
specifically, it relates to the application of certain phenomena and 
relationships of optics to the generation, detection and interpretation of 
scattered light diffraction patterns created by illuminating the surface 
of the specimen undergoing testing with coherent light. 
Surface finish roughness modifies the reflected light properties by 
introducing diffuse scattering superposed upon a specular reflection. The 
light appears speckled due to constructive and destructive interference 
fluctuations between coherent light waves scattered from surface 
irregularities. The distribution of scattered light is a direct 
consequence of surface roughness. 
The ability to quantify optically surface roughness measurements is of 
value in several areas; e.g., automatic sensing of surface qualities in 
hazardous and remote environments, as a diagnostic aid to evaluate tool 
wear and defects, quality control inspection, and automatic machining and 
finishing of critical parts. Noncontacting measurements and rapid response 
are features of importance. Practical usage requires surface quality 
inspection of machined metal specimens to be made rapidly over relatively 
large areas and in shop environments. 
Presently used methods have several drawbacks. Most rely heavily upon 
subjective machine operator or inspector skills and experience, the use of 
reference or comparison templates, contacting stylus mechanical devices 
such as PROFILOMETERS, or microscope interferometry techniques. Some other 
reflective optical procedures involve specimen motion, beam motion, or 
probe scanning. Unfortunately, such measurements are usually 
time-consuming and limited to small sample regions. 
It is apparent that the major limitations of the presently used methods are 
that they are labor intensive and the quality of the product varies with 
the skills of the technician. 
It is accordingly a general object of the present invention to provide a 
noncontacting method and apparatus for evaluating the surface roughness 
characteristics of a specimen. More specifically, it is an object of the 
invention to overcome the aforementioned limitations associated with the 
known techniques. 
It is a particular object of the invention to provide an optical method and 
apparatus for evaluating surface roughness characteristics of a specimen. 
Other objects will be apparent in the following detailed description and 
practice of the invention. 
SUMMARY OF THE INVENTION 
The foregoing and other objects and advantages which will be apparent in 
the following detailed description of the preferred embodiment, or in the 
practice of the invention, are achieved by the invention disclosed herein, 
which generally may be characterized as a method and apparatus for 
optically evaluating the surface roughness characteristics of a specimen 
having a surface characterized by Gaussian statistics, the method 
comprising the steps of: illuminating the surface of the specimen with a 
source of coherent light; forming on detecting means located in the far 
field a joint one-dimensional image and orthogonal Fourier transform 
spectrum distribution of the light scattered by the surface of the 
specimen, the joint distribution being characterized by a one-dimensional 
Gaussian function; and analyzing the shape of the joint one-dimensional 
image and orthogonal Fourier transform spectrum distribution to determine 
the surface roughness characteristics of the specimen; and the apparatus 
comprising; coherent light means for illuminating the surface of the 
specimen with coherent light; cylindrical-spherical lens means for forming 
on detecting means located in the far field a joint one-dimensional image 
and orthogonal Fourier transform spectrum distribution of the light 
scattered by the surface of the specimen, the joint distribution being 
characterized by a one-dimensional Gaussian function; and means for 
analyzing the shape of the joint one-dimensional image and orthogonal 
Fourier transform spectrum distribution to determine the surface roughness 
characteristics of the specimen.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
The present invention is based on the unique optical Fourier transform 
properties of lenses in coherent light. For a given optical setup, 
properties of the Fourier transform spectrum, or the diffraction pattern, 
of coherent light reflected from the surface of a specimen under 
investigation, such as distribution of energy, symmetries, or polarization 
depend upon the nature of the illuminated surface. The diffraction pattern 
for a smooth surface reflection depends upon the illumination aperture; 
for example, a well-known sinc function is obtained for a rectangular 
illumination aperture. For reflecting surfaces with increasing roughness, 
the diffraction for the reflected light becomes mottled and speckled. 
However, the average light distribution, i.e., average for a given sample 
area or for an ensemble of identical scatterers, is Gaussian in shape for 
a Gaussian rough surface. A measure of the Gaussian shape of the 
diffracted light distribution is linearly related to the surface roughness 
parameters of the specimen. 
It is well known that the characteristics of scattered light due to random, 
isotropic (Gaussian) surface roughness depends upon two surface 
parameters; namely the surface height roughness (e.g., average or rms 
height variation) and the correlation length (e.g., the spatial variation 
of the height profile). These quantities are usually denoted by the 
symbols .sigma. and .tau. respectively, in the literature. 
When the ratio of surface height roughness to wavelength, 2.pi. 
.sigma./.lambda., is much greater than one, the surface is said to be a 
rough scatterer. To a close approximation, the distribution of scattered 
light in the diffraction pattern is given by the following expression: 
##EQU1## 
where: I is the light intensity as a function of .chi., normalized to its 
value at .chi.=0; 
.chi. is the sine function of the scattering angle measured from the normal 
to the surface; and exp denotes the exponential function. 
It is noted that the theoretical distribution of scattered light in the 
diffraction pattern with angle is, on the average Gaussian in shape. The 
width of the Gaussian curve is proportional to the ratio .sigma./.tau. for 
the rough scatterer case. Hence, the optical system's measurement will 
also be proportional to .sigma./.tau., that is the average diffraction 
pattern distribution will be Gaussian in shape with a halfwidth 
proportional to the ratio .sigma./.tau.. 
For weak scatterers, on the other hand, the quantity 2.pi. .sigma./.lambda. 
is much less than one. As a first order approximation, the distribution of 
scattered light in the diffraction pattern is given by the following 
expression: 
##EQU2## 
where: I is the light intensity as a function of .chi., normalized to its 
value at .chi.=0; 
.chi. is the sine function of the scattering angle measured from the normal 
to the surface; 
and exp denotes the exponential function. 
It is noted that the scattered light angular distribution is also Gaussian 
in shape (as an average result). The width of the Gaussian curve is now 
proportional to terms that involve .sigma. and .tau., but not solely 
proportional to the ratio .sigma./.tau.. 
Thus, a measurement of the signature curve taken at two wavelengths for 
which 2.pi. .sigma./.tau. is either greater or less than one will enable 
one to determine .sigma. and .tau. and consequently completely specify the 
Gaussian random surface properties. 
In certain applications only a measurement of the surface height roughness 
.sigma. may be of interest. In these cases, one needs only a measurement 
of the signature curve at a single wavelength .lambda. for which the 
surface acts as a rough scatterer, and a preestablished calibration curve 
relating known roughness .sigma. and signature curve halfwidth. 
The far field diffraction pattern of light scattered by a small, rough 
surface area is obtained with a coherent optical system and used to 
quantify roughness measurements of surfaces. The distribution can be 
anisotropic due to tooling marks, preferential wear, etc. A cylinder lens 
forms a one-dimensional transform spectrum at favorable angular 
orientations about the optic axis with respect to the surface sample to 
circumvent this problem and provides useful spectrum averaging. 
A schematic representation of the optical surface roughness detection 
apparatus with a one dimension re-image capability for one-dimensional 
measurements, is illustrated in FIG. 1a. The light beam size used to 
illuminate an area of the specimen would be established by optical 
components and methods not shown in the figure. These components and 
methods are known to those experienced in the technology. Other 
modifications of the illustrated optical system may be apparent from the 
teachings of this system. For example, the beam splitting means may be 
eliminated and the illumination beam may be directed at an angle to the 
surface of the specimen. 
Referring to FIG. 1a, light from a source of coherent light 1, such as, for 
example, a laser, is deflected by means 2, such as, for example, a beam 
splitter, onto a surface of the specimen 3 undergoing inspection. Light 
that is reflected and scattered in two dimensions by the surface is 
gathered by a transform lens 4, and re-imaged in one direction by a 
cylindrical lens 5 whose focusing action is in the plane of the figure. 
The cylindrical lens 5 is positioned such that a one-dimensional image of 
the illuminated area is formed at the detector plane 6. The cylindrical 
lens 5 can be rotated about its optic axis to prealign this lens in a 
favorable angular orientation. The detector 6 is located in or near the 
back focal plane of the transform lens 4 such that components of the 
scattered light diffraction pattern normal to the plane of the figure (and 
thus unaffected by the cylindrical lens), are focused onto the detector. 
It is noted that other lens combinations can be used to vary the size of 
the cylindrical lens imagery and of the diffraction pattern by methods 
well known to those versed in the state-of-the-art. Similarly, it is noted 
that the position of the transform and cylinder lenses can be reversed to 
accommodate such design features as optical magnification, overall size, 
etc. The one dimension diffraction pattern can be measured and mapped with 
the aid of a scanning detector 7 (or with a fixed detector array). The 
mapped distribution of the scattered light diffraction pattern is 
presented to analyzer 8 for analysis and surface roughness signature 
recognition. 
The Gaussian shape, expressed as a halfwidth, or more accurately, the 
angular width of the diffraction pattern in spatial frequency units at the 
half power points, is known to be related to the surface roughness 
parameters .sigma. and .tau.. The laser wavelength .lambda. serves as a 
scaling parameter to alter the spread of the Gaussian shaped distribution 
of the scattered light. 
The complete surface can be covered by movement of the specimen relative to 
the laser beam by well known methods. The results of the measurements for 
each portion of the complete specimen can be stored in the analyzer 8 and 
processed after the full specimen has been surveyed. 
FIG. 1b is a schematic illustration of the optical surface roughness 
apparatus for two-dimensional measurements. Its operation is similar to 
the operation of the optical apparatus illustrated in FIG. 1a, except that 
it does not utilize a cylinder lens to reimage the two-dimensional light 
distribution formed by transform lens 4. This setup is conveniently 
utilized when the specimen to be evaluated has no tooling marks, 
scratches, etc., which would mar the surface and mask the measurement. In 
this case, the two-dimensional light distribution obtained by the 
transform lens alone is usually sufficient to permit quantitative 
evaluation of its surface roughness characteristics. 
The invention can be used with curved surfaces as well as planar regions, 
i.e., it may be adapted for utilization with surfaces that are curved in 
one direction, so-called cylinder surfaces. To accommodate other surface 
geometries, beam shaping optical components would be used to illuminate 
the specimen under test. 
A schematic representation of an optical surface roughness detection 
apparatus adapted to make measurements in a cylindrical or tapered hole is 
illustrated in FIG. 2a. As shown therein, a laser beam 1 passed through a 
beam splitter 2 and illuminates a curved reflector 9. For this 
application, the reflector has a conical reflection surface. The surface 
angle is such as to reflect the incident beam into a plane at about 90 
degrees from the original beam axis. The cone-reflected beam is incident 
upon the inner surface of the cylindrical hole 10 (shown in sectional 
view). Light is back reflected from the hole 10 to the conical reflection 
surface 9 and to the beam splitter 2. A ring like distribution of light in 
one-to-one correspondence with the inner surface of the hole is reflected 
off the surface of the beam splitter 2 and formed in a plane normal to the 
optic axis, such as plane 11. A transform lens 4 is used to form the 
diffraction pattern of the conically-illuminated surface on a detector 
plane 6. The radial distribution of light in the detection plane 6 normal 
to the optic axis will be Gaussian for a Gaussian roughness hole surface. 
The detected distribution of the scattered light is mapped and analyzed as 
described above. 
In the modification illustrated in FIG. 2b, an aperture with a slit 11a in 
the radial direction is used in conjunction with a cylinder lens 5. The 
action of the slit 11a-cylinder lens 5 combination is to allow only the 
light from a narrow region of the inner hole surface 10 to be analyzed. 
The approximate size of this region is determined by the geometric 
projection of the slit 11a onto the inner hole surface 10. The slit 
11a-cylinder lens 5 pair would be rotated about the optic axis in unison 
to sample different regions of the hole 10. Scattered light in the 
direction parallel to the slit narrow dimension is not affected by the 
cylinder lens 5, and by means of the transform lens 4, forms the 
diffraction pattern distribution to by analyzed. 
It is clear that the above description of the preferred embodiment in no 
way limits the scope of the present invention which is defined by the 
following claims.