BACKGROUND In one method of surface roughness measurement, a mechanical stylus traverses the surface to be measured with an electrical transducer reading the micromovement of the stylus. The readings obtained from this apparatus produce a standardized number value corresponding to the roughness of the surface measured.

This is the root mean square or a standard unit to specify surface roughness.

The conventional approach utilizing a stylus gauge has many disadvantages in the context of industrial or manufacturing applications. These include the delicate nature of the gauge producing unsatisfactory performance under rough service with many parts being gauged; the output signal does not yield a single signal output corresponding to surface roughness, but rather a continuously varying output as each surface irregularity is traversed, and accordingly an average dwell must be derived in order to provide a surface roughness indicator signal. In addition, the precise nature of the set up and alignment of the stylus and the test surface precludes good repeatability of readings obtainable in the factory environment where, typically with heavy building, vibrations are present.

Mechanical surface roughness measuring instruments also require a relatively high degree of skill and it is quite time consuming to obtain measurements.

For this reason, the usual approach in achieving quality control in the manufacture of parts is to sample parts within a production lot, with scrapping or reworking of the entire lot, if the surface roughness of the sample parts do not measure up to the proper standards. This is inefficient and wasteful since an error in set up or procedures of the machining or grinding operation may be allowed to continue for an entire lot before correction of the problem. In addition, the good parts within a lot are either scrapped or required to be reworked.

In one alternative approach, an optical method is used to measure the ratio of specular to diffuse light level reflected from the surface which roughness is to be determined, upon illuminating the surface with an incident beam from a light source.

The principle relied on is that the rougher the surface, the proportion of the light reflected specularly decreases as the surface becomes rougher.

Another method of surface roughness measurement based on the specular intensity alone uses the following theory-based relation for the intensity of light specularly reflected from a relatively smooth surface at a given angle d : where li = the intensity of specularly reflected light R = the reflectivity of smooth surface (dependent on color of samples) Io = the incident intensity on surface a = the rms surface roughness of surface 8 = the angle of incidence \= the wavelength of radiation Implicit in the development of this equation is a Gaussian distribution of surface irregularities, and that the wavelength of the electromagnetic waves are small with respect to the gross contours of the surface.

It can be seen that the angle of incidence 0, the reflectivity of the surface R due to color, and the intensity Io of the incident beam are all factors in addition to surface roughness which would control the intensity of the specularly reflected component of the incident beam. In order to eliminate the factor R, a parallel beam monochromatic light be directed at a surface at differing angles of incidence c, and with the intensity of the specularly reflected light at each of the angles of reflections sensed. If this is done, then the surface roughness may be described by the following equation (2): The intensity ratio then varies only as the surface roughness if the two incident angles 8 +l, the ratio of the incident intensities and the source wavelengths are unchanged.

Accordingly, the effect of variations in surface reflectivity due to color is removed such that the relative intensities correspond directly to surface roughness regardless of the reflectivity of the surface. It has been noted in previous methods that while a correspondence between the specular intensity and surface roughness would exist, a direct correlation with a in root mean square values may not directly be derivable. This is because the surface irregularities may or may not be distributed as assumed in a Gaussian distribution. Thus in previous methods resort to calibration using surfaces of standard roughness was required to determine a.

It would therefore be desirable to have a method and apparatus for the direct, non-contact measurement of surface roughness using an optical technique that gives a measurement of surface roughness without resort to calibration of the surface.

SUMMARY A optical method and apparatus for surface roughness measurement is provided that does not require resort to calibration with known roughness. The method and apparatus take advantage of the unexpected and surprising finding that the surface roughness may be determined from a transition region of a curve generated from an equation relating reflected intensity with angle of incidence.

It is therefore an object of the invention to provide a method of measuring surface roughness, comprising directing a light beam at a sequence of incidence angles (0i... °n) onto a surface, where i is the index counter of the incidence angle in the sequence from 0 to n, and n is the number of incidence angles; measuring an intensity I (ds) of at least a portion of said beam reflected from said surface for each incidence angle in said sequence; and determining a surface roughness value for said surface from values of said incidence angles and values of said intensities.

It is another object of the invention to provide an apparatus for measuring surface roughness, comprising: a light source directing a light beam at an incidence angle 8 onto a surface to be measured; a light detector measuring the intensity I (0) of at least a portion of said light beam reflected from said surface; said light beam movable such that said incidence angle 0 is variable over a sequence of angles (oui... n) between grazing and normal incidence to said surface, where i is the index counter of the incidence angle in the sequence from 0 to n, and n is the number of incidence angles; and a processing unit for recording and converting values of said incidence angles and values of intensity signals from said light detector into a surface roughness value for said surface.

These and other objects and advantages of the invention will become apparent upon reading the following description and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS FIGURE 1 shows a schematic representation of the surface roughness measurement apparatus.

FIGURE 2 shows typical response curves for A vs. 0.

DESCRIPTION It has now been found that a direct non-contact measurement of surface roughness may be made without calibration and independent of the surface type, as will be now be described.

In one embodiment, the invention includes an apparatus for measuring surface roughness. In this embodiment, the apparatus comprises a light source directing a light beam at an incidence angle 0 onto a surface to be measured, a light detector measuring the intensity I (0) of at least a portion of the light beam reflected from said surface, and a processing unit for recording and converting values of said incidence angles and values of intensity signals from said light detector into a surface roughness value for said surface. The light beam may be movable such that the incidence angle 0 is variable over a sequence of angles (j... n) between grazing and normal incidence to the measured surface, where i is the index counter of the incidence angle in the sequence from 0 to n, and n is the number of incidence angles.

To obtain a movable light beam, the light source may be mounted on a first platform, and the light detector mounted on a second platform, with the first and second platforms symmetrically movable with respect to a normal to the measured surface such that the incidence angle is continuously variable between grazing and normal incidence. More generally, the movable light beam of the apparatus may be obtained using any movable light source and movable light detector.

The apparatus may further comprise a first pinhole aperture located between the light source and the measured surface, a polarizer located between the first pinhole aperture and the light source, and a second pinhole aperture located between the measured surface and the light detector. In this embodiment, the light beam may be directed though the polarizer, the first pinhold aperture, and the second pinhole aperture. Depending on the disposition of the light source, the light detector, the polarizer and the first and second pinholes will be movable in concert with the movable light beam or stationary, as the particular optical design requires.

The processing unit may be any processing unit capable of converting input values of angle and light intensity into a value of surface roughness for the measured surface. The processing unit should be capable of calculating a sequence of quantities (A ;... An-)) corresponding to each successive pair {I (dus,), I (ds+z)} of reflected light intensities measured for a sequence of incidence angles of the light beam directed onto the measured surface, where Oi is one angle of incidence in the sequence of incidence angles, and ds+o is the next successive angle of incidence in the sequence of incidence angles. The processing unit may identify the a transition region of a curve of 0 vs A to determine the quantity he in the sequence (As... An-l). By transition region, it is meant a region of the curve defining a maximum, minimum, or inflection region. A transition region may be abrupt such as in a steep parabolic curve, or may be extended over an extended, approximately constant A value as in a plateau. The transition region may be identified by determining the derivative dA/dQ for the range of (Ai... An-,) and locating the region in the range of 6 for which dA/dO is approximately equal to zero. The value of A is then he, for dA/dO approximately equal to zero The value Ae may then be used by the processing unit to calculate a surface roughness value from a suitable correlation or formula for surface roughness as a funtion of intensity of and incidence angle.

In one embodiment, the processing unit may utilize the following formula for Ai as a function of reflected intensity and incidence angle where he is the transition value in the sequence (A,... An- ;), and the surface roughness is determined by calculating the surface roughness a value from o = [he]/2 and X is the mean wavelength of the light beam.

An embodiment of the apparatus is as shown in Figure 1. As shown in Figure 1, in one embodiment the apparatus for surface roughness measurement includes a coherent light source 1, a linear polarizer 2, a first pinhole 3, the surface being measured 5, a second pinhole aperture 6, a light detector 7, and a processing unit 9.

The first pinhole 3 is disposed between the coherent light source 1 and a measured rough surface 5, and second pinhole 6 is disposed in front of the light detector 7. The polarizer 2 linearly polarizes the coherent light illuminating the measure surface 90° or 45° to the plane of incidence. The polarization state of the light and shape of the pinhole 3 are set in a way to provide the optimal intensity distribution on the measufeed surface 5. The size and shape of the pinhole 6 is chosen to provide proper detection of light reflected from the measured surface 5. Incidence angle 8 at which the light falls on the surface 5 being measured and reflectance angle 0 at which the reflected light is detected are equal to each other and may be varied simultaneously and symmetrically ranging between normal (d = 0°) and grazing directions (d = 90°). For a number n of discrete and closely located angles of incidence over the movement range, the intensity of the light I (0) reflected from the measured surface 5 is collected along with the angle 8 at which the value I (0) was taken. For every intensity of the light I (8) reflected form the measured surface 5, except the last one, the processing unit 9 calculates a number n-1 of quantities A using the formula (2).

The processing unit 9 employs an algorithm to search through the number n-1 of calculated values A and identify the transition value De. The measured RMS roughness value Rq is obtained as Rq = [he]/Z The operation principle of the present invention is further described with reference to Figure 1. Coherent light source 1 with a polarizer 2 and a pinhole 3 are disposed on a moving platform 4. Light from coherent light source 1 goes through the polarizer 2 and first pinhole 3 to the measured surface 5. Moving platform 4 is rotatable around a point on the measured surface 5, such that the light beam from light source 1 with wavelength-A strikes the same point on surface 5 but at different angles 0 ranging from normal to grazing. Pinhole 6 and light detector 7 are disposed on another moving platform 8. Moving platform 8 moves symmetrically with moving platform 4 such that light striking surface 5 at incidence angle 0 and reflecting at reflectance angle 0 is detected by light detector 7. An intensity signal from light detector 7 goes to processing unit 9. The processing unit 9 has the ability to collect light intensity values from light detector 7 and control the movement of both platforms 4,8 according to a preset algorithm. To start a measurement cycle, moving platforms 4,8 are positioned such that the initial angle of incidence corresponds to approximately grazing or normal. Each light intensity value 1 (0) is collected along with the angle 0 for which it was taken. The incidence angle 0 is incremented to the next measurement position in the sequence of 0, followed by the measurement of 1 (0).

The measurement cycle stops when the moving platforms 4,8 reach the terminal 0, which may be normal or grazing or any 0 in between. After moving cycle is complete, the processing unit 9 calculates a number of quantities Ai using the collected intensity values 1 (8) of the light reflected from the measure surface 5.

Processing unit 9 searches through the number of calculated valued Ai and identifies the transition value hee The measured RMS roughness value Rq is then obtained from Rq = @ The coherent light source 1 may be any light source with coherence length enough to diffract on the surface profile. The coherence length is / A ?,, where), is the central wavelength of the light source and Ak is the bandwidth of the light source.

Typically, this value does not have to be more than lmm. Suitable light sources include gas lasers, solid state lasers, liquid lasers, semiconductor lasers, and the like.

Mercury bulb are also suitable. There are wavelength limitations for the coherent light used. One limitation comes from the fact that at shorter wavelengths, light diffracts not only on the surface profile but also on the atomic or molecular surface structure. Hence x-rays or gamma rays sources cannot be used. At longer wavelengths, the size of surface profile's imperfections become too small for wave to diffract. Moreover, surface materials gradually become transparent while the wavelength increases. For instance, plastics and ceramics are transparent to microwaves. Accordingly, the visible region of the light spectrum in the most suitable to use in the device.

The polarizer 2 may be any polarizing element letting linearly polarized light though. All types of polarizers can be used, including dichroic, crystal calcite, and the like.

The purpose of the pinhole aperture 3 is to reject all radiation modes of the light source 1, leaving the TEM,, mode only. It is typically of circular shape with a diameter corresponding to the size of the TEM, mode of the light source used. For instance, typical aperture diameters for semiconductor lasers are about 0.2 mm, and for gas lasers are about 0.8 mm. The theoretically calculated value of the aperture's diameter for mercury bulbs is about 0.03 mm.

The moving platforms 4,8 are any controllable motion systems moving simultaneously and symmetrically, and providing a feedback to the processing unit 9 about their current angular position.

The purpose of the second pinhole aperture 6 is to reject background noise and light scattered (not reflected) by the surface being measured in order to improve the signal-to-noise ratio of the light detector 7 and the surface being measured. The greater the distance, the greater the required aperture diameter. For example, at a distance of 50 mm, the diameter is about 0.8 mm. At a distance of 120 mm, the diameter is about 1.3 mm.

The light detector 7 is typically a device that produces electrical signal (current or voltage) proportional to the amount of light striking its photosensitive surface. It is desirable for light detector 7 to provide a linear response. In order for light detector 7 to measure adequately, the light detector 7 should provide a linear response (non-linearity within about 0.02%). Usually, the"light detector"consists of two parts: a detector and an amplifier. Various photometric elements are suitable for use in the light detector 7, including photodiode and amplifier, photomultipliers, bolometers, and the like.

The processing unit 9 may be any programmable or non-programmable logical piece capable of controlling the movement of the moving platforms 4,8 and- collecting intensity values from the light detector 7 and corresponding angle values.

In one embodiment processing unit 9 is a conventional personal computer or the like.

Any single chip controller or programmable logic matrix is also suitable.

The invention also includes within its scope a method for measuring surface roughness. In one embodiment, the method utilizes an apparatus for measuring surface roughness as herein described. More generally, the method comprises directing a light beam at a sequence of incidence angles (d n) onto a surface to be measured, where i is the index counter of the incidence angle in the sequence from 0 to n, and n is the number of incidence angles, measuring the intensity I (ds) of at least a portion of the beam reflected from the surface for each incidence angle in the sequence, and determining a surface roughness value for the surface from values of the incidence angles and values of the intensities.

In one embodiment, the method comprises determining the surface roughness value by calculating a sequence of quantities (As... An-l) corresponding to each successive pair {I (ds,), I (Oj+X)} of reflected intensities measured for the sequence of incidence angles, where Oi is one angle of incidence in the sequence of incidence angles, and As+l is the next successive angle of incidence in the sequence of incidence angles. An transition value he is then determined for the sequence (As... An-l) and a surface roughness is then determined from he.

In another embodiment, each Ai in the sequence (As... An-l) is calculated using the formula he is the transition value in the sequence (As... An-l). The step of determining the surface roughness is done by calculating the surface roughness a value from a = [A,] ", and A is the mean wavelength of the light beam.

The number n of data pairs {0j, I (dj)} taken in a measurement of surface roughness may range from a few to many depending on the resolution and accuracy desired for the given measurement. In general, the number n may range from about 10 to about 100. A greater number of data points taken will require a greater measurement time.

Calculation of the quantity may be done with a processing unit having a program suitable for calculation of output values from input values. Any suitable programming language may be used to design a suitable processing program, including but not limited to BASIC, FORTRAN, C++, Visual BASIC, and the like.

Generally, a suitable program may be designed for the calculation of a sequence of values (As... An-l) from an input array of n values for each of Oi and I (Oi).

Determination of the transition value he from the sequence of values (Ai On_) may be done using any of several methods known in the art. The transition region may be identified by determining the derivative d0/d6 for the range of (As...

An- ;) and locating the region in the range of 6 for which d0/d6 is approximately equal to zero. The value of A is then Ae, for d0/d6 approximately equal to zero.

Figure 2 illustrates typical shape of response curves for A vs 0. Generally, for surfaces of greater surface roughness, the transition region x will extend over a relatively short region of values, as seen in the region xl. For surfaces of lesser surface roughness, the the transition region will extend over a longer region of 8 values, as seen in the region X3. The curves as seen in Figure 2 are only representative are not intended to imply that these are the only possible responses. Indeed, the response of A vs 0 for small 0 may show large or small values of A, depending on the particular surface being measured and the increment in d. The dashed lines in Figure 2 indicate the shape of curves where large A are seen for small 0. A typical response curve for A vs A may show a plateau region corresponding to a maximum, minimum, or inflection in the curve. The transition value he for a given surface is taken as the relatively constant A value in a region x as shown in Figure 2.