CN117213391A - Optimal system error design method based on space carrier technology - Google Patents
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Abstract
The invention discloses an optimal system error design method based on a space carrier technology, which comprises the following steps: s1, acquiring a PV value of a surface to be measured of a mirror to be measured; s2, enabling the weight occupied by the system return error OPD to be equal to the weight occupied by the surface PV value to be measured, wherein the error range is +/-15%; s3, calculating the optimal inclination angle alpha of the mirror to be measured relative to the reference mirror; and S4, calculating the optimal carrier stripe number N corresponding to the optimal inclination angle alpha. According to the method for designing the optimal system error based on the space carrier technology, different numbers of carrier fringes can be introduced for different types and different specifications of mirrors to be tested, the system return error is controlled within a reasonable range, so that spectrum aliasing cannot occur in the subsequent phase extraction process, more surface shape information is reserved as much as possible, and the accuracy of measuring the surface shape by utilizing the SPSI technology is improved.
Description
Technical Field
The invention relates to the technical field of laser interference surface shape detection, in particular to an optimal system error design method based on a space carrier technology.
Background
The optical measurement is to acquire various physical quantities and technical parameters by using an optical method, and is widely applied to the field of surface shape detection by virtue of the characteristics of high precision, non-contact and the like. Phase-shifting interferometry (Phase Shifting Interferometry, PSI) plays an important role in optical measurements, and is divided into temporal phase shifting and spatial phase shifting, depending on the manner in which the phase is shifted. The time phase shift is realized by introducing phase shift quantity with equal step length at different moments, and the method has high measurement precision, but poor anti-interference capability, is only suitable for static measurement and does not meet the requirement of dynamic deformation measurement; the spatial phase shift is introduced from the airspace, and a phase diagram of the object in the state is usually calculated by using a single-frame interference diagram. Compared with the time phase shift, the space phase shift has strong anti-interference capability, the error caused by mechanical vibration and air flow interference can be negligibly small, and the acquisition time is allowed to be several orders of magnitude smaller than the time phase shift.
The Spatial Phase-shifting interference (SPSI) is the most applicable Spatial Phase-shifting technique at present, and the essential principle is that a proper amount of Spatial carrier is introduced by tilting the angle of a test beam relative to a reference beam, so that a high-frequency component with surface shape information to be detected is subjected to frequency shift on a frequency domain and separated from a low-frequency component containing background light information, thereby obtaining the Phase distribution of a detected wave surface. The number of carrier fringes is determined by the magnitude of the carrier quantity, and is generally limited by the conditions of spectrum separation degree, system backhaul error and the like. If the number of carrier fringes is too small, after the interference pattern is transformed from a space domain to a frequency domain, the high-order frequency spectrum and the low-order frequency spectrum are easy to be subjected to aliasing, so that the subsequent extraction of the high-order frequency spectrum and the reservation of more surface shape information are not facilitated; if the number of carrier fringes is too large, larger return errors are brought to the system, and finally the surface shape detection accuracy is reduced. The company ZYGO in the united states takes the default PPF (stripe pixel ratio) =8, i.e. a trade-off with a stripe width equal to 8 pixels width to determine the number of carrier stripes, which is determined primarily by the CCD resolution. However, it was found from practical measurements that this does not guarantee precision for all specifications of optical elements, especially for some spherical mirrors with large PV values. Therefore, how to select a proper number of carrier stripes is an important factor in achieving high-precision SPSI surface shape detection.
Disclosure of Invention
The invention aims to provide an optimal system error design method based on a space carrier technology, which can introduce different numbers of carrier fringes for different types and specifications of mirrors to be tested, control the system return error within a reasonable range, ensure that no spectrum aliasing occurs in the subsequent phase extraction process, keep more surface shape information as much as possible, and improve the accuracy of measuring the surface shape by utilizing an SPSI technology.
In order to achieve the above object, the present invention provides an optimal systematic error design method based on a spatial carrier technique, comprising the following steps:
s1, acquiring a PV value of a surface to be measured of a mirror to be measured;
s2, enabling the weight occupied by the system return error OPD to be equal to the weight occupied by the surface PV value to be measured, wherein the error range is +/-15%;
s3, calculating the optimal inclination angle alpha of the mirror to be measured relative to the reference mirror;
and S4, calculating the optimal carrier stripe number N corresponding to the optimal inclination angle alpha.
Preferably, in step S1, the obtaining the PV value of the surface to be measured of the mirror to be measured specifically includes:
if the mirror to be detected is a plane mirror, default PV value of the surface to be detected is equal to 0.3λ, where λ is light source wavelength;
if the mirror to be measured is a spherical mirror, calculating the PV value of the surface to be measured according to a calculation formula of the PV value of the spherical mirror, wherein the specific calculation formula of the PV value of the spherical mirror is as follows:
PV＝R-Rcosα＝R[1-cos(arcsinφ/2R)](1)，
wherein R is the curvature radius of the spherical mirror to be measured, and phi is the caliber of the spherical mirror to be measured.
Preferably, in step S3, the optimal tilt angle α of the mirror to be measured relative to the reference mirror is obtained by back-pushing a calculation formula of a system backhaul error, where a specific calculation formula of the system backhaul error is:
OPD＝l+(L+l)/cos2α-L (2)，
wherein L is the length of an inner cavity of the interferometer, L is the length of an outer cavity of the interferometer, and alpha is the inclination angle of the mirror to be measured relative to the reference mirror;
in the actual measurement calculation process, the use of the simplified formula of the formula (2) is simplified into:
OPD＝L(1/cos2α-1)(3)。
preferably, in step S4, the optimal carrier stripe number N is obtained by substituting the optimal tilt angle α into a carrier stripe number calculation formula, where the specific calculation formula of the carrier stripe number N is:
N＝D/ΔL＝2Dα/λ(4)，
wherein D is the aperture of an interferometer camera, deltaL is the interval between two adjacent stripes, alpha is the inclination angle of the mirror to be detected relative to the reference mirror, and lambda is the wavelength of the light source.
Therefore, the invention adopts the optimal system error design method based on the space carrier technology, and has the following beneficial effects:
(1) According to the optimal system error design method based on the space carrier technology, when the Fizeau interferometer is used for carrying out surface shape detection on the optical element, different numbers of carrier fringes can be introduced for different types and different specifications of mirrors to be detected, the system return error is controlled within a reasonable range, so that spectrum aliasing cannot occur in the subsequent phase extraction process, more surface shape information is reserved as much as possible, and the accuracy of measuring the surface shape by utilizing the SPSI technology is improved.
(2) According to the space carrier technology-based optimal system error design method, the weight of the system return error OPD is equal to the weight of the PV value of the mirror to be tested, the error range is within +/-15%, the PV value of the mirror to be tested is estimated, the introduced carrier quantity is determined according to the estimated PV value, and the carrier stripe numbers with different numbers are used for the mirrors to be tested with different specifications, so that the adaptive optimal system error introduction is realized.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a schematic flow chart of an algorithm of an embodiment of an optimal systematic error design method based on a spatial carrier technique;
FIG. 2 is a geometric schematic diagram of a sphere mirror PV value calculation formula of an embodiment of an optimal systematic error design method based on spatial carrier technology according to the present invention;
fig. 3 is a geometric schematic diagram of a calculation formula of a system backhaul error OPD according to an embodiment of a method for designing an optimal system error based on a spatial carrier technique;
fig. 4 is a geometric schematic diagram of a calculation formula of the carrier fringe number N according to an embodiment of the method for designing an optimal systematic error based on the spatial carrier technology.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs.
An optimal system error design method based on a space carrier technology is disclosed, wherein the optimal system error is determined by using the PV value of a mirror to be detected; the optimal system error is introduced by tilting the mirror to be measured to generate a relative tilt angle alpha with the reference mirror; finally, the optimal systematic error is characterized by the number of carrier stripes N.
As shown in fig. 1, an optimal systematic error design method based on spatial carrier technology includes the following steps:
s1, acquiring a PV value of a surface to be measured of a mirror to be measured, wherein the PV value is specifically as follows:
the mirror to be measured can be a plane mirror or a spherical mirror, if the mirror to be measured is a plane mirror, the PV value of the default surface to be measured is equal to 0.3λ, wherein λ is the wavelength of the light source;
if the mirror to be measured is a spherical mirror, the PV value of the surface to be measured is calculated by a spherical mirror PV value calculation formula, and the obtaining principle of the spherical mirror PV value calculation formula is shown in FIG. 2: wherein, the curvature radius OA of the spherical mirror is R, the caliber AB is phi, and the geometric relationship is that: the PV value of the spherical mirror is equal to the difference between OD and OC length. The specific expression is:
PV＝R-Rcosα＝R[1-cos(arcsinφ/2R)](1)，
wherein R is the curvature radius of the spherical mirror to be measured, and phi is the caliber of the spherical mirror to be measured.
S2, enabling the weight occupied by the system return error OPD to be equal to the weight occupied by the surface PV value to be measured, and enabling the error range to be within +/-15%.
And S3, calculating the optimal inclination angle alpha of the mirror to be detected relative to the reference mirror, wherein the optimal inclination angle alpha is obtained by back-pushing a system return error calculation formula. The principle of obtaining the specific calculation formula of the system return error is shown in fig. 3: the interferometer can be a Fizeau interferometer, L is the length of the inner cavity of the interferometer, namely the distance from the reference mirror RF to the CCD target surface; l is the external cavity length of the interferometer, i.e. the distance between the reference mirror and the test mirror; alpha is the relative inclination angle of the mirror to be measured and the reference mirror.
Two beams of light are emitted from the point O, the reference beam is reflected back to the CCD surface by the reference mirror, and the intersection point is A; the test light beam sequentially passes through the point C of the reference mirror and the point B of the mirror to be tested and is reflected back to the CCD surface, and the intersection point between the test light beam and the reference mirror is D during reflection. The optical path difference between the test beam and the reference beam can be expressed as: opd=oc+bc+bd=ob+bd. When the relative inclination angle of the mirror to be tested is alpha, the relative inclination angle of the test light beam and the reference mirror is 2 alpha. The expression of the system backhaul error OPD, which is derived from the geometry, is:
OPD＝l+(L+l)/cos2α-L(2)，
wherein L is the length of the inner cavity of the interferometer, L is the length of the outer cavity of the interferometer, and alpha is the inclination angle of the mirror to be measured relative to the reference mirror. In the actual measurement process, since the length L of the external cavity of the interferometer is far smaller than the length L of the internal cavity of the interferometer, L can be ignored in the calculation process, and the expression of the system return error OPD of the formula (2) can be simplified as follows:
OPD＝L(1/cos2α-1)(3)。
and S4, calculating the optimal carrier stripe number N corresponding to the optimal inclination angle alpha, and representing the optimal system error through the optimal carrier stripe number N. The optimal carrier stripe number N is obtained by substituting the optimal inclination angle alpha into a carrier stripe number calculation formula. The principle of obtaining the carrier stripe number N calculation formula is shown in fig. 4: the relative tilt angle of the test mirror TF and the reference mirror RF is α. After light is vertically incident from the reference mirror, interference fringes with alternate brightness are formed on the surface of the test mirror, and the optical path difference delta can be expressed as:
wherein n represents the refractive index of the medium between the reference mirror and the test mirror; e represents the distance from the carrier stripe on the test mirror to the plane of the reference mirror, i.e. the thickness of the carrier stripe.
From which the kth and the (k+1) th bright stripes are selected, assuming their thicknesses are e, respectively k And e k+1 The carry-over optical path difference expression is:
in the actual measurement process, the medium between the reference mirror and the mirror to be measured is air, and the refractive index n=1, so that the thickness difference deltae=λ2 between two adjacent bright stripes can be obtained by combining the two formulas. As can be derived from the geometric relationship, the spacing Δl between two adjacent stripes is:
if the caliber of the interferometer is D, the optimal carrier fringe number N is:
therefore, the invention adopts the optimal system error design method based on the space carrier technology, utilizes the PV value of the mirror to be detected to determine the number of the optimal carrier stripes to be introduced, controls the system return error within a reasonable range, ensures that no spectrum aliasing occurs in the subsequent phase extraction process, retains more surface shape information as much as possible, saves labor and time cost, and improves the accuracy and efficiency of measuring the surface shape by utilizing the SPSI technology.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (4)
1. An optimal system error design method based on a space carrier technology is characterized in that: the method comprises the following steps:
s1, acquiring a PV value of a surface to be measured of a mirror to be measured;
s2, enabling the weight occupied by the system return error OPD to be equal to the weight occupied by the surface PV value to be measured, wherein the error range is +/-15%;
s3, calculating the optimal inclination angle alpha of the mirror to be measured relative to the reference mirror;
and S4, calculating the optimal carrier stripe number N corresponding to the optimal inclination angle alpha.
2. The method for designing an optimal systematic error based on the spatial carrier technique according to claim 1, wherein: in step S1, the PV value of the surface to be measured of the mirror to be measured is obtained specifically as follows:
if the mirror to be detected is a plane mirror, default PV value of the surface to be detected is equal to 0.3λ, where λ is light source wavelength;
if the mirror to be measured is a spherical mirror, calculating the PV value of the surface to be measured according to a calculation formula of the PV value of the spherical mirror, wherein the specific calculation formula of the PV value of the spherical mirror is as follows:
PV＝R-Rcosα＝R[1-cos(arcsinφ2R)](1)，
wherein R is the curvature radius of the spherical mirror to be measured, and phi is the caliber of the spherical mirror to be measured.
3. The method for designing an optimal systematic error based on the spatial carrier technique according to claim 1, wherein: in step S3, the optimal tilt angle α of the mirror to be measured relative to the reference mirror is obtained by back-pushing a calculation formula of a system backhaul error, where the specific calculation formula of the system backhaul error is:
OPD＝l+(L+l)cos2α-L(2)，
wherein L is the length of an inner cavity of the interferometer, L is the length of an outer cavity of the interferometer, and alpha is the inclination angle of the mirror to be measured relative to the reference mirror;
in the actual measurement calculation process, the use of the simplified formula of the formula (2) is simplified into:
OPD＝L(1cos2α-1)(3)。
4. the method for designing an optimal systematic error based on the spatial carrier technique according to claim 1, wherein: in step S4, the optimal carrier stripe number N is obtained by substituting the optimal tilt angle α into a carrier stripe number calculation formula, where the specific calculation formula of the carrier stripe number N is:
N＝DΔL＝2Dαλ(4)，
wherein D is the aperture of an interferometer camera, deltaL is the interval between two adjacent stripes, alpha is the inclination angle of the mirror to be detected relative to the reference mirror, and lambda is the wavelength of the light source.
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