Techniques for determining the peak angle of response of piezoelectric crystals and other radiation-sensitive resonant devices

Claim 2

In a machine-instrumented method of determining the angle of peak amplitude response of a radiation-sensitive resonant device to a beam of radiation incident on a first surface of the device as the relative angle between the incident beam and the first surface is swept in a first direction, the improvement which comprises the steps of: scanning the first surface stepwise with the beam of radiation in the first direction; sampling the amplitude response of the device at the angle attained at the end of each step; storing successive ones of the measured amplitude samples; determining the attained angle of scan corresponding to each stored amplitude sample; determining the value of a first one of the attained angles occurring when the amplitude of the samples has decreased monotonically over a prescribed number of successive steps; retrieving a first one of the stored samples corresponding to a second one of the attained angles occurring the predetermined number of steps before the first attained angle; calculating a predetermined amplitude value equal to a prescribed percentage of the retrieved first amplitude sample; determining the value of a third one of the attained angles occurring when the samples have decreased in amplitude to the predetermined value following the first attained angle; determining the value of a fourth one of the attained angles corresponding to the predetermined value and occurring before the second attained angle; and averaging the third and fourth attained angles to approximate the angle of peak response of the device.

Claim 3

In a machine-instrumented method of determining the angle of peak amplitude response of a radiation-sensitive resonant device to a beam of radiation incident on a first surface of the device as the relative angle between the incident beam and the first surface is scanned in a first direction over the response characteristic of the device, the improvement which comprises the steps of: scanning the first surface stepwise with the beam of radiation in the first direction; sampling the amplitude response of the device at the angle attained at the end of each step; storing successive ones of the measured amplitude samples; determining the attained angle of scan corresponding to each stored amplitude sample; determining the value of a first one of the attained angles occurring when the amplitude of the samples has decreased monotonically over a prescribed number of successive steps; retrieving a first one of the stored samples corresponding to a second one of the attained angles occurring the predetermined number of steps before the first attained angle; calculating a first predetermined amplitude value equal to a prescribed percentage of the first sample; comparing, at the conclusion of successive steps starting with the step in which the amplitude of the samples has decreased to the first predetermined value following the first attained angle, the value of a then-occurring second one of the samples with a plurality of previously-stored third ones of the samples which individually correspond to third ones of the attained angles preceding the second attained angle, the third samples having amplitudes between the first predetermined value and a second predetermined value smaller than the first predetermined value; determining, during each comparing step, the value of the stored third attained angle corresponding to the third sample which is closest to the then-occurring second sample; adding each so-determined third attained angle to a fourth one of the attained angles corresponding to the thenoccurring second sample to form a first sum; terminating the comparing steps when the second amplitude sample has decreased in amplitude to the second predetermined value, whereby the number of first sums obtained is equal to the number of steps occurring between the first predetermined value and the second predetermined value following the first attained angle; adding the first sums to form a second sum; and dividing the second sum by twice the last-mentioned number of steps to approximate the angle of peak response of the device.

Claim 4

In a machine-instrumented method of determining the angle of peak amplitude response of a radiation-sensitive resonant device to a beam of radiation incident on a first surface of the device as the relative angle between the incident beam and the first surface is scanned in a first direction over the response characteristic of the device, the improvement which comprises the steps of: scanning the first surface stepwise with the beam of radiation in the first direction; sampling the amplitude response of the device at the angle attained at the end of each step; storing successive ones of the measured amplitude samples; determining the attained angle of scan corresponding to each stored amplitude sample; determining the value of a first one of the attained angles occurring when the amplitude of the samples has decreased monotonically over a prescribed number of successive steps; retrieving a first one of the stored samples corresponding to a second one of the attained angles occurring the predetermined number of steps before the first attained angle; calculating a first predetermined amplitude value equal to a prescribed percentage of the first sample; comparing, at the conclusion of successive steps starting with the step in which the amplitude of the samples has decreased to the first predetermined value following the first attained angle, the value of a then-occurring second one of the samples with a plurality of previously-stored third ones of the samples which individually correspond to third ones of the attained angles preceding the second attained angle, the third samples having amplitudes between the first predetermined value and a second predetermined value smaller than the first predetermined value; determining, during each comparing step, the value of the stored third attained angle corresponding to the third sample which is closest to the then-occurring second sample; adding each so-determined third attained angle to a fourth one of the attained angles corresponding to the thenoccurring second sample to form a first sum; terminating the comparing steps when the second amplitude sample has decreased in amplitude to the second predetermined value, whereby the number of first sums obtained is equal to the number of steps occurring between the first predetermined value and the second predetermined value following the first attained angle; adding the first sums to form a second sum; and dividing the second sum by twice the last-mentioned number of steps to approximate the angle of peak response of the device.

Claim 5

In a machine-instrumented method of determining the angle of peak reflection, from a prescribed internal atomic plane of a crystal, of a beam of radiation incident on the atomic plane through a reference surface of the crystal as the relative angle between the incident beam and the reference surface is scanned in a first direction over an angular range encompassing the response characteristic of the crystal to the beam, the improvement which comprises the steps of: scanning the first surface of the crystal stepwise with the beam of radiation in the first direction; sampling the amplitude of reflection of radiation from the crystal at the angle attained at the end of each step; storing successive ones of the measured amplitude samples; determining the attained angle of scan corresponding to each stored sample; determining the value of a first one of the attained angles occurring when the amplitude of the samples has decreased monotonically over a prescribed number of successive steps; retrieving a first one of the stored samples corresponding to a second one of the stored attained angles occurring the predetermined number of steps before the first attained angle; calculating first and second predetermined amplitude values individually equal to first and second prescribed percentages of the amplitude of the retrieved first sample, the first percentage being greater than the second percentage; comparing each of at least two second ones of the amplitude samples occurring after the first attained angle with a plurality of previously stored third ones of the samples which individually correspond to third ones of the attained angles preceding the second attained angle and which have amplitudes in the range between the first and second predetermined values, inclusive, the amplitudes of the second samples being in the range between the first and second predetermined values, inclusive; determining, during each comparing step, the value of the stored third attained angle corresponding to the third sample whose amplitude is closest to the then-occurring second sample; determining, during each comparing step, the value of a fourth one of the attained angles corresponding to the then-occurring second sample; adding all the third and fourth attained angles resulting from the comparing steps; and dividing the resulting sum by twice the number of second samples to approximate the angle of peak reflection from the crystal.

Claim 6

In a machine-instrumented method of determining the angle of peak reflection, from a prescribed internal atomic plane of a crystal, of a beam of radiation incident on the atomic plane through a reference surface of the crystal as the relative angle between the incident beam and the reference surface is scanned in a first direction over an angular range encompassing the response characteristic of the crystal to the beam, the improvement which comprises the steps of: scanning the first surface of the crystal stepwise with the beam of radiation in the first direction; sampling the amplitude of reflection of radiation from the crystal at the angle attained at the end of each step; storing successive ones of the measured amplitude samples; determining the attained angle of scan corresponding to each stored sample; determining the value of a first one of the attained angles occurring when the amplitude of the samples has decreased monotonically over a prescribed number of successive steps; retrieving a first one of the stored samples corresponding to a second one of the stored attained angles occurring the predetermined number of steps before the first attained angle; calculating first and second predetermined amplitude values individually equal to first and second prescribed percentages of the amplitude of the retrieved first sample, the first percentage being greater than the second percentage; comparing each of at least two second ones of the amplitude samples occurring after the first attained angle with a plurality of previously stored third ones of the samples which individually correspond to third ones of the attained angles preceding the second attained angle and which have amplitudes in the range between the first and second predetermined values, inclusive, the amplitudes of the second samples being in the range between the first and second predetermined values, inclusive; determining, during each comparing step, the value of the stored third attained angle corresponding to the third sample whose amplitude is closest to the then-occurring second sample; determining, during each comparing step, the value of a fourth one of the attained angles corresponding to the then-occurring second sample; adding all the third and fourth attained angles resulting from the comparing steps; and dividing the resulting sum by twice the number of second samples to approximate the angle of peak reflection from the crystal.

Claim 7

A method as defined in claim 3, in which the prescribed number of successive steps is two.

Claim 8

A method as defined in claim 3, in which the first predetermined value is equal to 871/2% of the amplitude of the first sample.

Claim 9

A method as defined in claim 5, in which the second predetermined value is equal to 50% of the amplitude of the first sample.

Claim 10

A method as defined in claim 3, in which the scanning step is accomplished by passing a fixed beam of the radiation through the reference surface as the reference surface is incrementally advanced in the first direction.

Claim 11

A method as defined in claim 3, in which the radiation comprises a beam of X-rays.

Claim 12

In a machine-instrumented method of determining the angle of peak reflection, from a prescribed internal atomic plane of a piezoelectric crystal, of a beam of radiation directed toward the atomic plane through the reference surface of the crystal as a relative angle between the incident beam and the first surface is swept in a first direction over an angular range encompassing the response characteristic of the crystal to said beam, the improvement which comprises the steps of: scanning the reference surface stepwise with the beam of radiation in the first direction; sampling the amplitude of the radiation reflected from the crystal at the angle attained at the end of each step; storing the measured amplitude samples occurring after the amplitude response exceeds a first predetermined amplitude value; determining the attained angle of scan corresponding to each stored amplitude sample; determining the value of a first one of the attained angles occurring when the amplitude of the successive samples has decreased monotonically over a prescribed number of successive steps; retrieving a first one of the stored samples corresponding to a second one of the attained angles occurring the predetermined number of steps before the first attained angle; calculating a second predetermined amplitude value equal to a first prescribed percentage of the amplitude of the first sample; calculating a third predetermined amplitude value equal to a second prescribed percentage of the amplitude of the first sample, the second percentage being lower than the first percentage; comparing, at the conclusion of each successive step starting with the step in which the amplitude sample has decreased to the second predetermined value following the first attained angle, the amplitude of a then-occurring second one of the samples with a plurality of previously stored third ones of the samples which individually correspond to attained values preceding the second attained value and which have amplitudes in the range extending from the second predetermined value to the third predetermined value, inclusive; retrieving, from each comparison, the successive pair of third samples having amplitudes immediately greater and less than the amplitude of the then-occurring second sample; deriving, from the so-determined successive pair of third samples, the value of a third one of the attained angles occurring before the second attained angle and corresponding to the amplitude of the second sample; adding each so-derived third attained angle to a fourth one of the attained angles corresponding to the then-occurring second sample to form a first sum; terminating the comparison when the fourth sample had decreased in amplitude to the third predetermined value, whereby the number of first sums obtained is equal to the number of steps occurring between the second predetermined value and the third predetermined value following the occurrence of the first attained angle; adding the first sums to form a second sum; and dividing the second sum by twice the last-mentioned number of steps to approximate the angle of peak reflection of the crystal.

Claim 13

In a machine-instrumented method of determining the angle of peak reflection, from a prescribed internal atomic plane of a piezoelectric crystal, of a beam of radiation directed toward the atomic plane through the reference surface of the crystal as a relative angle between the incident beam and the first surface is swept in a first direction over an angular range encompassing the response characteristic of the crystal to said beam, the improvement which comprises the steps of: scanning the reference surface stepwise with the beam of radiation in the first direction; sampling the amplitude of the radiation reflected from the crystal at the angle attained at the end of each step; storing the measured amplitude samples occurring after the amplitude response exceeds a first predetermined amplitude value; determining the attained angle of scan corresponding to each stored amplitude sample; determining the value of a first one of the attained angles occurring when the amplitude of the successive samples has decreased monotonically over a prescribed number of successive steps; retrieving a first one of the stored samples corresponding to a second one of the attained angles occurring the predetermined number of steps before the first attained angle; calculating a second predetermined amplitude value equal to a first prescribed percentage of the amplitude of the first sample; calculating a third predetermined amplitude value equal to a second prescribed percentage of the amplitude of the first sample, the second percentage being lower than the first percentage; comparing, at the conclusion of each successive step starting with the step in which the amplitude sample has decreased to the second predetermined value following the first attained angle, the amplitude of a then-occurring second one of the samples with a plurality of previously stored third ones of the samples which individually correspond to attained values preceding the second attained value and which have amplitudes in the range extending from the second predetermined value to the third predetermined value, inclusive; retrieving, from each comparison, the successive pair of third samples having amplitudes immediately greater and less than the amplitude of the then-occurring second sample; deriving, from the so-determined successive pair of third samples, the value of a third one of the attained angles occurring before the second attained angle and corresponding to the amplitude of the second sample; adding each so-derived third attained angle to a fourth one of the attained angles corresponding to the then-occurring second sample to form a first sum; terminating the comparison when the fourth sample had decreased in amplitude to the third predetermined value, whereby the number of first sums obtained is equal to the number of steps occurring between the second predetermined value and the third predetermined value following the occurrence of the first attained angle; adding the first sums to form a second sum; and dividing the second sum by twice the last-mentioned number of steps to approximate the angle of peak reflection of the crystal.

Claim 14

A method as defined in claim 9, in which the deriving step comprises retrieving the values of the attained angles respectively corresponding to the determined successive third samples, determining the amplitude difference between the value of the then-occurring fourth sample and one of the corresponding retrieved third samples, and interpolating between the values of the determined attained angles corresponding to said determined successive third samples in accordance with the ratio of said determined amplitude difference to the actual amplitude difference between the successive third samples to obtain the third attained angle.

Claim 15

A method as defined in claim 9, in which the scanning step comprises stepping the beam of radiation at a relatively high angular rate from an initial angle spaced from the angular range of the device characteristic to an attained angle corresponding to the first predetermined amplitude value, and thereafter stepping the beam in the first direction at a relatively slow angular rate.

Claim 16

In an apparatus for determining the angle of peak reflection, from a prescribed internal atomic plane of a piezoelectric crystal, of a beam of radiation directed toward the atomic plane through a reference surface of the crystal as the relative angle between the incident beam and the reference surface is scanned over an angular range encompassing the response characteristic of the crystal, wherein the apparatus comprises a detector for measuring the amplitude of reflection from the crystal and means for indicating the instantaneous attained angle of the crystal during the scan, the improvement which comprises, in combination: means for stepping the reference surface with respect to the beam of radiation to vary the output of the detector; quantizing means operative at the stepping rate for sampling the output of the detector; a memory; means for coupling the successive samples from the quantizing means to the memory; means coupled to the stepping means for coupling the output of the angle indicating means to the memory; means including delay means responsive to the successive samples for generating a first indication when the amplitude of the successive samples has decreased monotonically over N successive steps; first means associated with the memory and responsive to the first indication for retrieving a stored first one of the samples from the memory corresponding to a first one of the attained angles occurring N steps prior to the step in which the first indication is generated; means coupled to the first retrieving means for individually multiplying the retrieved first sample by a first relatively high and a second relatively low prescribed fraction to obtain first and second predetermined values, respectively; means associated with the storing means and rendered effective during each of a plurality of first steps when the amplitude of the successive samples lies between the first and second predetermined values following the generation of the first indication for scanning previously stored second ones of the amplitude samples occurring in the amplitude range extending between the first and second predetermined values, inclusive, and corresponding to attained angles preceding the first attained angle; second means responsive to the first scanning means and operative during each of the first steps for retrieving a pair of successive values of the second samples that are respectively greater and less than the amplitude of a then-occurring third one of the samples; third means rendered effective upon the retrieval of each of said pair of successive second samples for retrieving a pair of third successive attained angles corresponding to said pair of retrieved second samples; means responsive to the second and third retrieving means for deriving a fourth one of the attained angles occurring between the successive pair of retrieved third angles; means operative during the successive first steps for accumulating all the values of the successively derived fourth attained angles and the values of successive fifth ones of the attained angles corresponding to each third sample; and means for dividing the output of the accumulating means by twice the number of first steps to generate a quotient indicative of the angle of peak reflection of the crystal.

Claim 17

In an apparatus for determining the angle of peak reflection, from a prescribed internal atomic plane of a piezoelectric crystal, of a beam of radiation directed toward the atomic plane through a reference surface of the crystal as the relative angle between the incident beam and the reference surface is scanned over an angular range encompassing the response characteristic of the crystal, wherein the apparatus comprises a detector for measuring the amplitude of reflection from the crystal and means for indicating the instantaneous attained angle of the crystal during the scan, the improvement which comprises, in combination: means for stepping the reference surface with respect to the beam of radiation to vary the output of the detector; quantizing means operative at the stepping rate for sampling the output of the detector; a memory; means for coupling the successive samples from the quantizing means to the memory; means coupled to the stepping means for coupling the output of the angle indicating means to the memory; means including delay means responsive to the successive samples for generating a first indication when the amplitude of the successive samples has decreased monotonically over N successive steps; first means associated with the memory and responsive to the first indication for retrieving a stored first one of the samples from the memory corresponding to a first one of the attained angles occurring N steps prior to the step in which the first indication is generated; means coupled to the first retrieving means for individually multiplying the retrieved first sample by a first relatively high and a second relatively low prescribed fraction to obtain first and second predetermined values, respectively; means associated with the storing means and rendered effective during each of a plurality of first steps when the amplitude of the successive samples lies between the first and second predetermined values following the generation of the first indication for scanning previously stored second ones of the amplitude samples occurring in the amplitude range extending between the first and second predetermined values, inclusive, and corresponding to attained angles preceding the first attained angle; second means responsive to the first scanning means and operative during each of the first steps for retrieving a pair of successive values of the second samples that are respectively greater and less than the amplitude of a then-occurring third one of the samples; third means rendered effective upon the retrieval of each of said pair of successive second samples for retrieving a pair of third successive attained angles corresponding to said pair of retrieved second samples; means responsive to the second and third retrieving means for deriving a fourth one of the attained angles occurring between the successive pair of retrieved third angles; means operative during the successive first steps for accumulating all the values of the successively derived fourth attained angles and the values of successive fifth ones of the attained angles corresponding to each third sample; and means for dividing the output of the accumulating means by twice the number of first steps to generate a quotient indicative of the angle of peak reflection of the crystal.

Claim 18

Apparatus as defined in claim 12, in which the means for coupling the samples to the memory includes normally disabled gating means rendered effective when the amplitude of the successive samples have attained a third predetermined value indicative of a threshold level of the crystal response characteristic.

Claim 19

Apparatus as defined in claim 12, in which the deriving means comprises, in combination, means for determining the relative amplitude difference between said then-occurring third sample and one of the correspondingly retrieved successive second samples, fourth means for retrieving the fifth pair of attained angles corresponding to the successive second samples, and means coupled to the output of the amplitude difference determining means and the fourth retrieving means for interpolating between said successive fifth angles in accordance with said relative amplitude difference to define the fourth one of said attained angles.