US5488476A
Expired / Lapsed
US
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Apparatus and method using optical diffraction to measure surface roughness
Assignee: Taylor Hobson Ltd
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Filing: 1994-10-12
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Granted: 1996-01-30
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Expires: 2014-10-12
Abstract
Abstract Apparatus for measuring surface roughness utilizes diffraction patterns derived from the surface under test. The energies in the different orders are detected and processed utilizing various different algorithms dependent upon a number of factors such as the number of orders in the diffraction pattern and asymmetry in the diffraction pattern. Various filter functions both for the diffraction pattern itself and for values of surface roughness after measurement are disclosed. One algorithm for measuring surface roughness involves comparison of values representing the energy orders with reference values, preferably reference values obtained by an interpolation operation between one set of reference values representative of a diffraction pattern from a symmetrical surface and another set representative of a diffraction pattern from an asymmetrical surface.
Inventors
- 👤 Daniel Mansfield
- 👤 Ian Bell
- 👤 Ian Buehring
- 👤 Jennifer Harding
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-29 14:12
CPC Classifications
G; G01; G01B; G01B11/00; G01B11/30; G01B11/303
Claims Analysis
Total Claims: 72
Claim 1
Independent Claim
130 words
Apparatus for measuring surface roughness of a workpiece comprising: a) means for illuminating the workpiece to produce a diffraction pattern; b) means for determining a set of values dependent upon the energy distribution in said pattern; c) means for providing, for each of a plurality of values of surface roughness, a set of interpolated reference values representing the energy distribution in a diffraction pattern, said set of reference values being obtained by interpolation between first and second sets of reference values representing the energy distributions in diffraction patterns obtained respectively from relatively symmetrical and relatively asymmetrical surfaces; and d) means for comparing the set of values determined from said diffraction pattern produced by the workpiece with said set of interpolated reference values to obtain an indication of said surface roughness.
Claim 2
Dependent Claim
130 words
Apparatus for measuring surface roughness of a workpiece comprising: a) means for illuminating the workpiece to produce a diffraction pattern; b) means for determining a set of values dependent upon the energy distribution in said pattern; c) means for providing, for each of a plurality of values of surface roughness, a set of interpolated reference values representing the energy distribution in a diffraction pattern, said set of reference values being obtained by interpolation between first and second sets of reference values representing the energy distributions in diffraction patterns obtained respectively from relatively symmetrical and relatively asymmetrical surfaces; and d) means for comparing the set of values determined from said diffraction pattern produced by the workpiece with said set of interpolated reference values to obtain an indication of said surface roughness.
Claim 3
Dependent Claim
31 words
Apparatus according to claim 1, comprising means for determining the degree of asymmetry in the diffraction pattern obtained from the workpiece and performing said interpolation on the basis of said asymmetry.
Claim 4
Dependent Claim
54 words
Apparatus according to claim 2, comprising means for rebuilding the energy distribution in the values representing the orders in the diffraction pattern derived from the workpiece utilizing polynomials whose coefficients are selected dependent upon said degree of asymmetry and dependent upon the number of orders in the diffraction pattern derived from the work piece.
Claim 5
Dependent Claim
46 words
Apparatus according to claim 3, wherein said comparison comprises deriving a function representing a plot against variation in Rq of the difference between the values derived from the workpiece and said sets of reference values and identifying minima in said plot, wherein Rq is surface roughness.
Claim 6
Dependent Claim
40 words
Apparatus according to claim 4, wherein if the diffraction pattern derived from the workpiece has only zero and one or both first orders, the surface roughness value corresponding to the smallest minimum value in said function is taken as correct.
Claim 7
Dependent Claim
72 words
Apparatus according to claim 4, wherein, if said diffraction pattern derived from said workpiece has at least a second, third or fourth order and there is only one minimum in said function, the corresponding value of surface roughness is taken as the correct one if it fails within a range indicated by comparing the energies in the zero orders of first and second diffraction patterns derived from the workpiece at different wavelengths.
Claim 8
Dependent Claim
90 words
Apparatus according to claims 4, wherein, if the diffraction pattern obtained from the workpiece includes at least a second, third or fourth order and there is only one minimum in said function, if the value of surface roughness indicated by said one minimum disagrees with a range indicated by comparing the energies in the zero orders of first and second diffraction patterns obtained from the workpiece at different wavelengths, said function is differentiated to locate a point of inflection and said point of inflection utilized in determination of surface roughness.
Claim 9
Dependent Claim
71 words
Apparatus according to claim 4, wherein, if said diffraction pattern derived from said workpiece contains at least a second, third or fourth order and there is only one minimum in said function and said minimum indicates a value for surface roughness within the range 70 to 120 nanometers, the function having a flat bottom within the region of said minimum, the value for surface roughness is obtained utilizing a linear equation.
Claim 10
Dependent Claim
222 words
Apparatus according to claim 4, wherein if said function has a plurality of minima indicating respective different possible values for surface roughness, the smallest possible value for surface roughness is taken as correct if this is less than or equal to 25 nanometers; that value of surface roughness which is closest to 88 nanometers is taken as correct if comparison of the energies in the zero orders of first and second diffraction patterns obtained from the workpiece at different wavelengths indicates a value close to 88 nanometers; if said comparison of said energy in said zero orders suggests that surface roughness is not close to 88 nanometers, the number of possible values of surface roughness which conform to the result of said comparison is determined and: (i) if there is only one such value, this is taken as correct; (ii) if there are several possible such values, the one closest to 88 nanometer is taken as correct if said comparison indicates that surface roughness is relatively close to 88 nanometers and the one furthest from 88 nanometers is taken as correct if said comparison indicates that the value is remote from 88 nanometers; and (iii) if none of said possible values of surface roughness is in agreement with said comparison then that which is closest to 88 nanometers is taken as correct.
Claim 11
Dependent Claim
14 words
Apparatus according to claim 1, wherein said relatively symmetrical surface is a sinusoidal surface.
Claim 12
Dependent Claim
14 words
Apparatus according to claim 1, wherein said relatively symmetrical surface is of cusp-like form.
Claim 13
Dependent Claim
14 words
Apparatus according to claim 1, wherein said relatively symmetrical surface is of triangular form.
Claim 14
Dependent Claim
14 words
Apparatus according to claims 1, wherein said relatively asymmetrical surface is of saw-tooth form.
Claim 15
Dependent Claim
71 words
Apparatus according to claim 1, wherein said set of interpolated reference values are representative of the energy distribution in diffraction patterns which would be obtained from theoretical surfaces and wherein said processing means includes means for performing a value rebuilding step which takes into account low level diffracted energy arising in the diffraction pattern derived from the workpiece prior to comparing the values derived from the workpiece with the reference values.
Claim 16
Dependent Claim
18 words
Apparatus according to claim 14, wherein said value rebuilding step comprises rebuilding the values derived from the workpiece.
Claim 17
Dependent Claim
41 words
Apparatus according to claim 15, wherein said rebuilding step comprises rebuilding a value representing each order respectively utilizing a polynomial in which the values of the orders in the diffraction pattern derived from the workpiece are multiplied by coefficients and added.
Claim 18
Dependent Claim
21 words
Apparatus according to claim 16, wherein said coefficients are pre-calculated and derived from a multiplicity of surfaces having different surface characteristics.
Claim 19
Dependent Claim
19 words
Apparatus according to claim 17, wherein said multiplicity of surfaces from which said coefficients are derived are simulated surfaces.
Claim 20
Dependent Claim
108 words
Apparatus according to claim 17, wherein said derivation of said coefficients comprises deriving from said multiplicity of surfaces data representing the energy distribution in diffraction patterns which would be produced from such surfaces utilizing said apparatus, calculating the surface roughness of such multiplicity of surfaces, deriving sets of reference values for said multiplicity of surfaces utilizing said surface roughness as calculated, and relating the values representing the energy distribution of the diffraction patterns derived from said multiplicity of surfaces with said reference values derived for said multiplicity of surfaces by polynomial equations comprising unknown coefficients and obtaining best fit values for said unknown coefficients utilizing a mathematical technique.
Claim 21
Dependent Claim
15 words
Apparatus according to claim 19, wherein said mathematical technique is a least means squares method.
Claim 22
Dependent Claim
45 words
Apparatus according to claim 19, wherein said values representing said energy distribution in said diffraction patterns derived from said multiplicity of surfaces are divided into groups dependent upon the orders in said diffraction patterns and different sets of coefficients are derived for said different groups.
Claim 23
Dependent Claim
27 words
Apparatus according to claim 21, wherein said groups are further divided according to the degree of asymmetry of said diffraction patterns derived from said multiplicity of surfaces.
Claim 24
Dependent Claim
22 words
Apparatus according to claim 1, wherein said interpolation is performed according to the asymmetry in the diffraction pattern derived from the workpiece.
Claim 25
Dependent Claim
35 words
Apparatus according to claim 23, wherein said asymmetry in said diffraction pattern derived from said workpiece is obtained by summing the differences in the energies in the different pairs of orders in the diffraction pattern.
Claim 26
Dependent Claim
27 words
Apparatus according to claim 23, wherein said asymmetry is quantized, said quantization being utilized in selecting the coefficients derived from the multiplicity of surfaces in said group.
Claim 27
Dependent Claim
126 words
Apparatus for measuring a surface characteristic of a workpiece comprising: a) means for illuminating the workpiece to produce a diffraction pattern; b) means for deriving a plurality of signals dependent upon the energy distribution in said pattern; c) means defining a plurality of algorithms with which said signals may be processed for determining said surface characteristics; d) means for selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein a first algorithm is selected if said diffraction pattern has substantially only a zero order, and a second algorithm is selected if said diffraction pattern contains substantial energy in orders other than the zero order; and e) processing means for processing said signals with the selected algorithm to obtain said surface characteristic.
Claim 28
Dependent Claim
126 words
Apparatus for measuring a surface characteristic of a workpiece comprising: a) means for illuminating the workpiece to produce a diffraction pattern; b) means for deriving a plurality of signals dependent upon the energy distribution in said pattern; c) means defining a plurality of algorithms with which said signals may be processed for determining said surface characteristics; d) means for selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein a first algorithm is selected if said diffraction pattern has substantially only a zero order, and a second algorithm is selected if said diffraction pattern contains substantial energy in orders other than the zero order; and e) processing means for processing said signals with the selected algorithm to obtain said surface characteristic.
Claim 29
Dependent Claim
37 words
Apparatus according to claim 26, wherein said selecting means is operative to count the orders in the diffraction pattern after discarding energy levels less than a predetermined percentage of the maximum energy level detected in said pattern.
Claim 30
Dependent Claim
11 words
Apparatus according to claim 27, wherein said predetermined percentage is 10%.
Claim 31
Dependent Claim
54 words
Apparatus according to claim 26, including means for providing, for each of a plurality of values of surface roughness, a set of reference values representing the energy distribution in a diffraction pattern, wherein said second algorithm comprises comparing a set of values dependent upon the energy distribution in said pattern with said reference values.
Claim 32
Dependent Claim
62 words
Apparatus according to claim 29, wherein said reference values are derived by interpolation between a first set of reference values representative of the energy distribution in a diffraction pattern which would be produced from a relatively symmetrical surface and a second set of reference values representing the energy distribution in a diffraction pattern which would be produced from a relatively asymmetrical surface.
Claim 33
Dependent Claim
59 words
Apparatus according to claim 26, wherein said first algorithm comprises calculating Rq from the Gaussian Algorithm formula ##EQU31## wherein λ is representative of the wavelength of said illumination and Sn is representative of the energy in the zero order of said diffraction pattern, wherein said selecting means selects said formula when said diffraction pattern comprises only the zero order.
Claim 34
Dependent Claim
31 words
Apparatus according to claim 31, comprising means for performing a filtering operation on a set of signals representing the diffraction pattern comprising only the zero order prior to applying said formula.
Claim 35
Dependent Claim
146 words
Apparatus for measuring a surface characteristic of a workpiece comprising: a) means for illuminating the workpiece to produce a diffraction pattern; b) means for deriving a plurality of signals dependent upon the energy distribution in said pattern; c) means defining a plurality of algorithms with which said signals may be processed for determining said surface characteristic; d) means for selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein one of said algorithms comprises calculating Rq from the Gaussian Algorithm formula ##EQU32## wherein λ is representative of the wavelength of said illumination and Sn is representative of the energy in the zero order of said diffraction pattern; and wherein said selecting means selects said formula when said diffraction pattern comprises only the zero order; and e) processing means for processing said signals with the selected algorithm to obtain said surface characteristic.
Claim 36
Dependent Claim
146 words
Apparatus for measuring a surface characteristic of a workpiece comprising: a) means for illuminating the workpiece to produce a diffraction pattern; b) means for deriving a plurality of signals dependent upon the energy distribution in said pattern; c) means defining a plurality of algorithms with which said signals may be processed for determining said surface characteristic; d) means for selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein one of said algorithms comprises calculating Rq from the Gaussian Algorithm formula ##EQU32## wherein λ is representative of the wavelength of said illumination and Sn is representative of the energy in the zero order of said diffraction pattern; and wherein said selecting means selects said formula when said diffraction pattern comprises only the zero order; and e) processing means for processing said signals with the selected algorithm to obtain said surface characteristic.
Claim 37
Independent Claim
125 words
A method for measuring surface roughness of a workpiece comprising the steps of: a) illuminating said workpiece to produce a diffraction pattern; b) determining a set of values dependent upon the energy distribution in said pattern; c) providing for each of a plurality of values of surface roughness a set of reference values representing the energy distribution in a diffraction pattern, said set of reference values being obtained by the step of interpolation between first and second sets of reference values representing the energy distributions in diffraction patterns obtained respectively from relatively symmetrical and relatively asymmetrical surfaces; and d) comparing the sets of values determined from said diffraction pattern produced by the workpiece with said reference values to obtain an indication of said surface roughness.
Claim 38
Independent Claim
125 words
A method for measuring surface roughness of a workpiece comprising the steps of: a) illuminating said workpiece to produce a diffraction pattern; b) determining a set of values dependent upon the energy distribution in said pattern; c) providing for each of a plurality of values of surface roughness a set of reference values representing the energy distribution in a diffraction pattern, said set of reference values being obtained by the step of interpolation between first and second sets of reference values representing the energy distributions in diffraction patterns obtained respectively from relatively symmetrical and relatively asymmetrical surfaces; and d) comparing the sets of values determined from said diffraction pattern produced by the workpiece with said reference values to obtain an indication of said surface roughness.
Claim 39
Dependent Claim
34 words
The method according to claim 34, further comprising the step of determining the degree of asymmetry in the diffraction pattern obtained from the workpiece and performing said interpolation on the basis of said asymmetry.
Claim 40
Dependent Claim
56 words
The method according to claim 35, further comprising the step of rebuilding the energy distribution in the values representing the orders in the diffraction pattern derived from the workpiece utilizing polynomials whose coefficients are selected dependent upon said degree of asymmetry and dependent upon the number of orders in the diffraction pattern derived from the workpiece.
Claim 41
Dependent Claim
51 words
The method according to claim 36, wherein said step of comparing the step of deriving a function representing a plot against variation in Rq of the difference between the values derived from the workpiece and said sets of reference values and identifying minima in said plot, wherein Rq is surface roughness.
Claim 42
Dependent Claim
41 words
The method according to claim 37, wherein if said diffraction pattern derived from said workpiece has only zero and one or both first orders, the surface roughness value corresponding to the smallest minimum value in said function is taken as correct.
Claim 43
Dependent Claim
73 words
A method according to claim 37, wherein if said diffraction pattern derived from said workpiece has at least a second, third or fourth order and there is only one minimum in said function, the corresponding value of surface roughness is taken as the correct one if it falls within a range initiated by comparing the energies in the zero orders of first and second diffraction patterns derived from the workpiece at different wavelengths.
Claim 44
Dependent Claim
91 words
A method according to claim 37, wherein if said diffraction pattern obtained from the workpiece includes at least a second, third or fourth order and there is only one minimum in said function, if the value of surface roughness indicated by said one minimum disagrees with a range indicated by comparing the energy in the zero orders of first and second diffraction patterns obtained from the workpiece at different wavelengths, said function is differentiated to locate a point of inflection, said point of inflection being utilized in determining the surface roughness.
Claim 45
Dependent Claim
69 words
A method according to claim 37, wherein if said diffraction pattern derived from said workpiece contains at least a second, third or fourth order and there is only one minimum in said function and said minimum indicates a value for surface roughness within the range 70-120 nanometers, the function having a flat bottom within the region of said minimum, the value for surface roughness obtained utilizing a linear equation.
Claim 46
Dependent Claim
217 words
A method according to claim 37, wherein if said function has a plurality of minima indicating respective different possible values for surface roughness, the smallest possible value of surface roughness is taken as correct if this is less than or equal to 25 nanometers; that value of surface roughness which is closest to if comparison of the energies in the zero orders of first and second diffraction patterns obtained from said workpiece at different wavelengths indicates a value close to 88 nanometers; if said comparison of said energy in said zero orders suggest that surface roughness is not close to 88 nanometers, the number of possible values of surface roughness which conform to the result of said comparison is determined and; (i) if there is only one such value, this is taken as correct; (ii) if there are several possible such values, the one closest to 88 nanometers is taken as correct if said comparison indicates that surface roughness is relatively close to 88 nanometers and the one furthest from 88 nanometers is taken as correct if said comparison indicates that the value is remote from 88 nanometers; and (iii) if none of said possible values of surface roughness is in agreement with said comparison then that which is closest to 88 nanometers is taken as correct.
Claim 47
Dependent Claim
15 words
A method according to claim 34, wherein said relatively symmetrical surface is a sinusoidal surface.
Claim 48
Dependent Claim
15 words
A method according to claim 34 wherein said relatively symmetrical surface is of cusp-like form.
Claim 49
Dependent Claim
15 words
A method according to claim 34, wherein said relatively symmetrical surface is of triangular form.
Claim 50
Dependent Claim
16 words
A method according to claim 34, wherein said relatively asymmetrical surface is of a saw-tooth form.
Claim 51
Dependent Claim
68 words
A method according to claim 34, wherein reference values are representative of the energy distribution in diffraction patterns which would be obtained from theoretical surfaces and wherein said processing means includes means for performing a value rebuilding step which takes into account low level diffracted energy arising in the diffraction pattern derived from the workpiece prior to comparing of values derived from said workpiece with the reference values.
Claim 52
Dependent Claim
19 words
A method according to claim 34, wherein said value rebuilding step comprises rebuilding the values derived from the workpiece.
Claim 53
Dependent Claim
42 words
A method according to claim 48, wherein said rebuilding step comprises rebuilding a value representing each order respectively utilizing a polynomial in which the values of the orders in the diffraction pattern derived from the workpiece are multiplied by coefficients and added.
Claim 54
Dependent Claim
22 words
A method according to claim 49, wherein said coefficients are pre-calculated and derived from a multiplicity of surfaces having different surface characteristics.
Claim 55
Dependent Claim
20 words
A method according to claim 50, wherein said multiplicity of surfaces from which said coefficients are derived are simulated surfaces.
Claim 56
Dependent Claim
111 words
A method according to claim 50, wherein said derivation of said coefficients comprises the steps of deriving from said multiplicity of surface data representing the energy distribution in diffraction patterns which would be produced from such surfaces utilizing said apparatus, calculating the surface roughness of such multiplicity of surfaces, deriving sets of reference values for said multiplicity of surfaces utilizing said surface roughness as calculated, and relating the values representing the energy distribution of diffraction patterns derived from said multiplicity of surfaces with said reference values derived from said multiplicity of surfaces by polynomial equations comprising unknown coefficients and obtaining best fit values for said unknown coefficients utilizing a mathematical technique.
Claim 57
Dependent Claim
16 words
A method according to claim 52, wherein said mathematical technique is a least means squares method.
Claim 58
Dependent Claim
46 words
A method according to claim 52, wherein said values representing said energy distribution in said diffraction patterns derived from said multiplicity of surfaces are divided into groups dependent upon the orders in said diffraction patterns and different sets of coefficients are derived for said different groups.
Claim 59
Dependent Claim
28 words
A method according to claim 54, wherein said groups are further divided according to the degree of asymmetry of said diffraction patterns derived from said multiplicity of surfaces.
Claim 60
Dependent Claim
25 words
A method according to claim 34, wherein said step of interpolation is performed according to the asymmetry in the diffraction pattern derived from the workpiece.
Claim 61
Dependent Claim
39 words
A method according to claim 56, wherein said asymmetry in said diffraction pattern derived from said workpiece is obtained by the step of summing the differences in the energies in the different pairs of orders in the diffraction pattern.
Claim 62
Dependent Claim
28 words
A method according to claim 56, wherein said asymmetry is quantized, said quantization being utilized in selecting the coefficients derived from the multiplicity of surfaces in said group.
Claim 63
Independent Claim
120 words
A method for measuring a surface characteristic of a workpiece comprising the steps of: a) illuminating the workpiece to produce a diffraction pattern; b) deriving a plurality of signals dependent upon the energy distribution in said pattern; c) defining a plurality of algorithms with which said signals may be processed for determining said surface characteristics; d) selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein a first algorithm is selected if said diffraction pattern has substantially only a zero order, and a second algorithm is selected if said diffraction pattern contains substantial energy in orders other than the zero order; and e) processing said signals with the selected algorithm to obtain said surface characteristic.
Claim 64
Independent Claim
120 words
A method for measuring a surface characteristic of a workpiece comprising the steps of: a) illuminating the workpiece to produce a diffraction pattern; b) deriving a plurality of signals dependent upon the energy distribution in said pattern; c) defining a plurality of algorithms with which said signals may be processed for determining said surface characteristics; d) selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein a first algorithm is selected if said diffraction pattern has substantially only a zero order, and a second algorithm is selected if said diffraction pattern contains substantial energy in orders other than the zero order; and e) processing said signals with the selected algorithm to obtain said surface characteristic.
Claim 65
Dependent Claim
41 words
A method according to claim 59, wherein said step of selecting an algorithm is operative to count the orders in the diffraction pattern after discarding energy levels less than a predetermined percentage of the maximum energy level detected in said pattern.
Claim 66
Dependent Claim
12 words
A method according to claim 60, wherein said predetermined percentage is 10%.
Claim 67
Dependent Claim
56 words
A method according to claim 59, including the step of providing, for each of a plurality of values of surface roughnesses, a set of reference values representing the energy distribution in a diffraction pattern, wherein said second algorithm comprises comparing a set of values dependent upon the energy distribution in said pattern with said reference values.
Claim 68
Dependent Claim
66 words
A method according to claim 62, wherein said reference values are derived by the step of interpolation between a first set of reference values representative of the energy distribution in a diffraction pattern which would be produced from a relatively symmetrical surface and a second set of reference values representing the energy distribution in a diffraction pattern which would be produced from a relatively asymmetrical surface.
Claim 69
Dependent Claim
60 words
A method according to claim 59, wherein said first algorithm comprises calculating Rq from the Gaussian Algorithm formula ##EQU33## wherein λ is representative of the wavelength of said illumination and Sn is representative of the energy in the zero order of said diffraction pattern, wherein said selecting means selects said formula when said diffraction pattern comprises only the zero order.
Claim 70
Dependent Claim
32 words
Apparatus according to claim 64, comprising the step of performing a filtering operation on a set of signals representing the diffraction pattern comprising only the zero order prior to applying said formula.
Claim 71
Independent Claim
138 words
A method of measuring a surface characteristic of a workpiece comprising: a) illuminating the workpiece to produce a diffraction pattern; b) deriving a plurality of signals dependent upon the energy distribution in said pattern; c) defining a plurality of algorithms with which said signals may be processed for determining said surface characteristic; d) selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein one of said algorithms comprises calculating Rq from the Gaussian Algorithm formula ##EQU34## wherein λ is representative of the wavelength of said illumination and Sn is representative of the energy in the zero order of said diffraction pattern; and wherein said step of selecting selects said formula when said diffraction pattern comprises only the zero order; and e) processing said signals with the selected algorithm to obtain said surface characteristic.
Claim 72
Independent Claim
138 words
A method of measuring a surface characteristic of a workpiece comprising: a) illuminating the workpiece to produce a diffraction pattern; b) deriving a plurality of signals dependent upon the energy distribution in said pattern; c) defining a plurality of algorithms with which said signals may be processed for determining said surface characteristic; d) selecting an algorithm from said plurality dependent upon the orders in the diffraction pattern, wherein one of said algorithms comprises calculating Rq from the Gaussian Algorithm formula ##EQU34## wherein λ is representative of the wavelength of said illumination and Sn is representative of the energy in the zero order of said diffraction pattern; and wherein said step of selecting selects said formula when said diffraction pattern comprises only the zero order; and e) processing said signals with the selected algorithm to obtain said surface characteristic.
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