CN116625529A - Wide-range high-precision differential wavefront sensing measurement device - Google Patents
Wide-range high-precision differential wavefront sensing measurement device Download PDFInfo
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- CN116625529A CN116625529A CN202310739598.5A CN202310739598A CN116625529A CN 116625529 A CN116625529 A CN 116625529A CN 202310739598 A CN202310739598 A CN 202310739598A CN 116625529 A CN116625529 A CN 116625529A
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- 238000005259 measurement Methods 0.000 title claims abstract description 69
- 238000001514 detection method Methods 0.000 claims description 13
- 238000006243 chemical reaction Methods 0.000 claims description 12
- 230000010287 polarization Effects 0.000 claims description 12
- 230000035559 beat frequency Effects 0.000 claims description 8
- 238000005070 sampling Methods 0.000 claims description 7
- 239000000835 fiber Substances 0.000 claims description 3
- 238000001914 filtration Methods 0.000 claims description 3
- 238000010586 diagram Methods 0.000 description 11
- 239000013307 optical fiber Substances 0.000 description 9
- 230000003287 optical effect Effects 0.000 description 4
- 238000005516 engineering process Methods 0.000 description 3
- 230000000087 stabilizing effect Effects 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000001427 coherent effect Effects 0.000 description 1
- 230000008878 coupling Effects 0.000 description 1
- 238000010168 coupling process Methods 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
- Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation
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Abstract
The application provides a wide-range high-precision differential wavefront sensing measurement device, which enables a reference beam to enter a differential wavefront sensing unit through the reflection of a first spectroscope group and the beam combination of a measuring beam, wherein a certain included angle is formed between a spectroscope in the first spectroscope group and a horizontal plane, and the included angle between each spectroscope in the first spectroscope group and the horizontal direction is adjusted, so that the included angle between the reference beams is set, and the multi-frequency mixing is utilized, so that the measurement of a wide angle range is realized while the high precision is ensured, and the device has the characteristics of reasonable and simple structural design, high measurement precision, wide range and high stability.
Description
Technical Field
The application belongs to the optical precision measurement technology, and particularly relates to a wide-range high-precision differential wavefront sensing measurement device.
Background
The differential wavefront sensing measurement is an angle measurement technology based on heterodyne laser interference, and the basic principle is that two beams of laser with stable difference frequency are simultaneously incident on a four-quadrant detector and meet the coherence condition, four paths of beat signals can be generated, the four paths of beat signals record coherent light information received by corresponding quadrants respectively, phase information of the four paths of beat signals can be obtained through signal processing, and angle measurement of the two beams of laser can be realized by combining phase angle conversion coefficients.
The differential wavefront sensor has the advantages of high measurement precision, strong anti-interference capability, small coupling and the like, and is widely applied to high-precision laser interference application. The technology can achieve high measurement accuracy of the nrad magnitude, but because of periodic nonlinear errors of heterodyne laser interference, when the offset angle of signal light and local oscillation light is increased to a certain degree, a single differential wavefront sensing device can cause phase ambiguity to be unable to measure when a photoelectric detector solves the phase difference, and the angle measurement range can only reach the mrad magnitude. How to achieve an increased measurement range for differential wavefront sensing while maintaining high accuracy is a problem to be solved.
Disclosure of Invention
Based on the above, the application provides a wide-range high-precision differential wavefront sensing measurement device, which can realize wide-angle range measurement while ensuring high precision, and has high measurement precision.
The application relates to a wide-range high-precision differential wavefront sensing measuring device, which comprises:
the device comprises a laser source, a first spectroscope group, a differential wavefront sensing unit and a measuring and calculating module;
the laser source generates a reference beam which irradiates the first spectroscope group, and the reference beam is reflected by the first spectroscope group and combined with the measuring beam to enter the differential wavefront sensing unit;
the differential wavefront sensing unit is configured to output beat frequency signals to the measuring and calculating module based on the incident light beams;
and the measuring module is configured to calculate the included angle between the measuring beam and the reference beam according to the beat frequency signal.
The number of spectroscopes in the first spectroscope group is the same as the number of reference beams, so that each reference beam is reflected by an independent spectroscope;
and adjusting the included angle between each spectroscope in the first spectroscope group and the horizontal direction to ensure that the included angle between two adjacent reference beams is in a preset range, thereby realizing the expansion of the angle measurement range.
Further, the preset range is that the included angle of two adjacent reference beams is larger than half of the larger value in the measuring ranges corresponding to the two reference beams respectively and smaller than half of the sum of the measuring ranges corresponding to the two adjacent reference beams.
Further, the differential wavefront sensing unit comprises a four-quadrant photoelectric detection circuit, and the reference beam and the measuring beam are combined and then are incident to a photosensitive surface of the four-quadrant photoelectric detection circuit to form a beat frequency signal.
Further, the measuring and calculating module at least comprises:
the device comprises a photoelectric conversion unit, an AD sampling unit, a digital phase meter and an angle resolving unit;
a photoelectric conversion unit configured to convert a beat signal into an electric signal;
an AD sampling unit configured to convert the electric signal output from the photoelectric conversion unit into a digital signal;
a digital phase meter configured to calculate phase information of the reference beam and the measuring beam from the digital signal;
and an angle calculating unit configured to calculate an angle between the measuring beam and the reference beam based on the phase information.
Further, the measuring module further includes:
the adjustable gain control unit and the anti-aliasing filtering unit are arranged between the photoelectric conversion unit and the digital phase meter.
Further, the device also comprises a collimation module which is arranged between the laser source and the first spectroscope group and is used for collimating the reference beam incident to the first spectroscope group.
Further, the collimation module comprises a polarization maintaining optical fiber and a collimation lens, and the reference beam firstly passes through the polarization maintaining optical fiber along the light propagation direction and then enters the first spectroscope group through the collimation lens.
Further, the device also comprises an acousto-optic frequency shifter arranged between the laser source and the collimation module.
Further, the apparatus further includes a second beam splitter set disposed behind the laser source and configured to split the laser beam emitted by the laser source into at least two reference beams with equal light intensity.
Further, the measuring beam is formed by reflecting laser emitted by the laser source through the second beam splitter group.
The wide-range high-precision differential wavefront sensing measuring device has the following beneficial effects:
the wide-range high-precision differential wavefront sensing measurement device provided by the application has the advantages that the reference beam is reflected by the first spectroscope group and then is combined with the measuring beam to enter the differential wavefront sensing unit, wherein a certain included angle is formed between the spectroscope in the first spectroscope group and the horizontal plane, and the included angle between each spectroscope in the first spectroscope group and the horizontal direction is adjusted, so that the included angle between the reference beams is set, the multi-frequency mixing is utilized, the measurement in a wide-angle range is realized while the high precision is ensured, and the structure design is reasonable and simple, and the device has the characteristics of high measurement precision, wide range and high stability; the beat frequency signal passes through the same measuring and calculating module, has good noise common mode rejection capability, and effectively improves the measurement accuracy of the differential wavefront angle.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present application, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a wide-range high-precision differential wavefront sensing measurement apparatus according to a first embodiment of the present application;
FIG. 2 is a schematic illustration of the device of FIG. 1 for enlarging the measuring range during angle measurement;
FIG. 3 is a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device according to a second embodiment of the present application;
FIG. 4 is a schematic illustration of the expansion of the measurement range when angle measurement is performed using the apparatus illustrated in FIG. 3;
FIG. 5 is a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device according to a third embodiment of the present application;
FIG. 6 is a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device according to a fourth embodiment of the present application;
FIG. 7 is a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device according to a fifth embodiment of the present application;
fig. 8 is a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device according to a sixth embodiment of the present application.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Example 1
As shown in fig. 1, a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device according to this embodiment is provided with two unpolarized reference beams. The two-dimensional angle measuring device comprises a frequency stabilization laser (1), a spectroscope BS1 (2), a first acousto-optic frequency shifter AOM1 (3), a first polarization maintaining optical fiber (4), a first collimating lens (5), a spectroscope BS2 (6), a second acousto-optic frequency shifter AOM2 (7), a second polarization maintaining optical fiber (8), a second collimating lens (9), a spectroscope BS3 (10), a spectroscope BS4 (11), a spectroscope BS5 (12), a four-quadrant photoelectric detection circuit (13), a photoelectric conversion unit (14), an adjustable gain control unit (15), an anti-aliasing filter unit (16), an AD sampling unit (17), a digital phase meter (18), a two-dimensional angle resolving unit (19) and a two-dimensional angle result output unit (20) which are sequentially arranged along the light propagation direction.
The frequency-stabilized laser (1) generates laser with frequency f, and the laser is divided into a beam of transmitted light and a beam of reflected light by a spectroscope BS1 (2), wherein the transmitted light enters a first acousto-optic frequency shifter AOM1 (3) to obtain the laser with frequency f 1 Is coupled into a first polarization maintaining optical fiber (4), exits from a first collimating lens (5), is reflected by a spectroscope BS (11) and is transmitted by a spectroscope BS (5) 12, and is irradiated on a photosensitive surface of a four-quadrant photoelectric detection circuit (13). The reflected light obtained by the spectroscope BS1 (2) is reflected by the spectroscope BS2 (6) to enter the second sound frequency shifter AOM2 (7) to obtain the frequency f 2 Is coupled into a second polarization maintaining optical fiber (8), is emitted from a second collimating lens (9), is reflected by a spectroscope BS3 (10) and is transmitted by a spectroscope BS4 (11) and a spectroscope BS5 (12), and is irradiated on a photosensitive surface of a four-quadrant photoelectric detection circuit (13). Frequency f 1 、f 2 And a reference beam of frequency f 0 The measuring beams of the four-quadrant photoelectric detection circuit (113) are all incident on the photosensitive surface of the four-quadrant photoelectric detection circuit to generate heterodyne interference, and three beat frequencies are respectively |f 1 -f 0 |、|f 2 -f 0 |、|f 2 -f 1 Interference signal of.
The three beat signals with different frequencies output by the four-quadrant photoelectric detection circuit (13) respectively pass through a photoelectric conversion unit (14), an adjustable gain control unit (15), an anti-aliasing filter unit (16), an AD sampling unit (17) and a digital phase meter (18), phase information of measuring light beams and reference light beams is obtained according to different frequencies of the beat signals, and a two-dimensional angle result output unit (20) outputs a result through a two-dimensional angle calculation unit (19).
The beam splitter BS4 (11) and the beam splitter BS3 (10) respectively form alpha with the horizontal direction 1 、α 2 So that the two reference beams reflected by the lens have a fixed angle θ=α 2 -α 1 . The angle between the reference beams should be set to be greater than half the measurement range of each reference beam and less than half the sum of the measurement ranges of the two reference beams, in which case the angle θ is greater than the frequency f in the case shown in FIG. 1 1 Reference beam and frequency f 2 Reference beam respective measuring rangesHalf of the larger value of (1) and less than the sum of the two ranges +.>Half of (a) is provided.
It should be understood that the measurement ranges mentioned above refer to the range in which the angle measurement result of the measurement light is measurable when the measurement light interferes with a certain beam of reference light, such as the frequency f 1 The measurement range of the reference beam refers to the measurable range of the angle of the measuring light when the reference beam interferes with the measuring beam, and the physical value of the angle measurement result is still the included angle between the reference beam and the measuring beam, so that the angle measurement result reflects the angle change of the measuring light relative to the initial position. Reference is made to this definition for "measurement ranges" in the following description.
After the included angle between the measuring beam and a certain reference beam is increased to a certain extent, the phase ambiguity is caused when the photoelectric detector solves the phase difference, so that the measurement cannot be performed, the fixed included angle is in the set range, as shown in fig. 2, when the measuring beam is at the frequency f 1 Included angle of reference beam exceeds its rangeAt the time, the frequency f can be entered 2 Measuring range of reference beam->In such a way that the actual measuring range of the device can be extended to the sum of the measuring ranges of the differential wavefront sensing of the two reference beams +.>Effectively increases the differential wavefront sensing range.
It will be readily appreciated that the different reference beams may be generated by separate frequency stabilized lasers or may be generated by the same laser source.
In a further embodiment, under the condition that the beat frequency does not exceed the bandwidth range of the four-quadrant photoelectric detection circuit, the number of reference beams with different angles and different frequencies can be increased or reduced appropriately, the range of the differential wavefront sensing measurement device is enlarged or reduced, and wide-range high-precision two-dimensional angle measurement is realized.
In addition, the acousto-optic frequency shifter can be replaced by an electro-optic frequency shifter and other instruments which can also realize the adjustment of laser frequency.
Example two
As shown in fig. 3, the structure of the wide-range high-precision differential wavefront sensing measurement apparatus provided in this embodiment is different from that of the first embodiment in that three non-polarized reference beams are provided in this embodiment, and accordingly, a beam splitter BS6 (21), a third acousto-optic frequency shifter AOM3 (22), a third polarization maintaining optical fiber (23), a third collimating lens (24) and a beam splitter BS7 (25) are added, and laser generated by the frequency stabilizing laser (1) is reflected by the beam splitter BS1 (2) and transmitted by the beam splitter BS2 (6), and enters the third acousto-optic frequency shifter AOM3 (22) to obtain a frequency f 3 Is coupled into a third polarization maintaining optical fiber (23), is emitted from a third collimating lens (24), is reflected by a spectroscope BS7 (25) and is transmitted by a spectroscope BS3 (10), a spectroscope BS4 (11) and a spectroscope BS5 (12), is beaten on a photosensitive surface of a four-quadrant photoelectric detection circuit (13), and is heterodyned with a measuring beam and two other reference beams to form six beat frequencies of |f respectively 1 -f 0 |、|f 2 -f 0 |、|f 3 -f 0 |、|f 2 -f 1 |、|f 3 -f 1 |、|f 3 -f 2 Interference signal of.
Similarly, in this embodiment, similar to the embodiment, the beat signals of the six different frequencies output by the four-quadrant photoelectric detection circuit (13) respectively pass through the photoelectric conversion unit (14), the adjustable gain control unit (15), the anti-aliasing filtering unit (16), the AD sampling unit (17) and the digital phase meter (18), according to the difference of the frequencies of the beat signals, the phase information of the measuring light beam and each reference light beam is obtained, and the two-dimensional angle result is output by the two-dimensional angle result output unit (20) through the resolution of the two-dimensional angle resolving unit (19).
Spectroscope BS4 (11), spectroscope BS3 (10) and divisionThe mirrors BS7 (25) respectively form alpha with the horizontal direction 1 、α 2 、α 3 So that the frequency f reflected by the beam splitter BS4 (11), the beam splitter BS3 (10) and the beam splitter BS7 (25) 1 And f 2 Has a fixed angle theta 1 ＝α 2 -α 1 Frequency f 2 And f 3 Has a fixed angle theta 2 ＝α 3 -α 2 . Included angle theta 1 Is required to be greater than the frequency f 1 Reference beam and frequency f 2 Reference beam respective measuring rangesHalf of the larger value of (a) and less than the sum of the two rangesIs half of the included angle theta 2 Is required to be greater than the frequency f 2 Reference beam and frequency f 3 Reference beam respective measuring range->Half of the larger value of (1) and less than the sum of the two ranges +.>Half of (a) is provided.
After the included angle between the measuring beam and a certain reference beam is increased to a certain extent, the phase ambiguity is caused when the photo detector solves the phase difference, so that the measurement cannot be performed, and the fixed included angle is within the set range, as illustrated in fig. 4, when the measuring beam is at the frequency f 1 Included angle of reference beam exceeds its rangeAt the time, the frequency f can be entered 2 Measuring range of reference beam->In, measuring beam and frequency f 2 The included angle of the reference beam exceeds its range +.>At the time, the frequency f can be entered 3 Measuring range of reference beam->In that the differential wavefront angle measuring ranges between the measuring beam and the reference beams can be accumulated continuously segment by segment, i.e. the actual measuring range of the device can be extended to the sum of the measuring ranges of differential wavefront sensing of the three reference beams +.>Effectively increases the differential wavefront sensing range.
Example III
As shown in fig. 5, a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device provided in this embodiment is different from the foregoing embodiments in that four unpolarized reference beams are provided in this embodiment, and accordingly, a beam splitter BS8 (26), a fourth acousto-optic frequency shifter AOM4 (27), a fourth polarization maintaining optical fiber (28), a fourth collimating lens (29) and a beam splitter BS9 (30) are added.
The propagation of the reference beam and the processing and angular measurement of the optical signal are similar to those of the previous embodiments and will not be repeated here.
Example IV
As shown in fig. 6, a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device provided in this embodiment is different from that in the second embodiment in that three polarized reference beams are set in this embodiment, and accordingly, the beam splitter BS5 (12) is replaced by a polarized beam splitter PBS (31) and an analyzer (32) is added. The propagation of the reference beam and the processing and angular measurement of the optical signal are similar to those of the previous embodiments and will not be repeated here.
Example five
Fig. 7 is a schematic diagram of a wide-range high-precision differential wavefront sensing measurement device according to the present embodiment. Unlike the previous embodiments, the measurement beam of the present embodiment is from a remote satellite (33), and the propagation of the reference beam and the processing and angular measurement of the optical signal are similar to those of the previous embodiments and are not repeated here.
Example six
As shown in fig. 8, a schematic structural diagram of a wide-range high-precision differential wavefront sensing measurement device for laboratory precision angle measurement is provided in this embodiment.
The difference from the foregoing embodiment is that the measuring beam of the present embodiment is generated by the frequency stabilizing laser (1), and the apparatus of the present embodiment further includes a reflecting mirror (34), a fifth acousto-optic frequency shifter AOM5 (35), a fifth polarization maintaining fiber (36), a fifth collimating lens AOM5 (37), and a turning mirror (38) on the basis of the second embodiment.
The above embodiments are only for illustrating the technical solution of the present application, and are not limiting; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art will appreciate that: the technical scheme described in the foregoing embodiments can be modified or some of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application.
Claims (10)
1. The utility model provides a wide-range high accuracy difference wavefront sensing measuring device which characterized in that includes:
the device comprises a laser source, a first spectroscope group, a differential wavefront sensing unit and a measuring and calculating module;
the laser source generates a reference beam to irradiate the first spectroscope group, and the reference beam is reflected by the first spectroscope group and is combined with the measuring beam to be incident on the differential wavefront sensing unit;
the differential wavefront sensing unit is configured to output beat frequency signals to the measuring and calculating module based on the incident light beams;
the measuring module is configured to calculate the included angle between the measuring beam and the reference beam according to the beat signal;
the number of spectroscopes in the first spectroscope group is the same as the number of the reference beams, so that each reference beam is reflected by an independent spectroscope;
and adjusting the included angle between each spectroscope in the first spectroscope group and the horizontal direction to ensure that the included angle between two adjacent reference beams is in a preset range, thereby realizing the expansion of the angle measurement range.
2. The wide-range high-precision differential wavefront sensing measurement device of claim 1, wherein the preset range is that an included angle of two adjacent reference beams is greater than half of a larger value of measurement ranges corresponding to the two reference beams, and less than half of a sum of measurement ranges corresponding to the two adjacent reference beams.
3. The wide-range high-precision differential wavefront sensing measurement device of claim 1, wherein the differential wavefront sensing unit comprises a four-quadrant photo-detection circuit, and the reference beam and the measuring beam are combined and then incident on a photosensitive surface of the four-quadrant photo-detection circuit to generate a beat signal.
4. The wide-range high-precision differential wavefront sensing measurement device of claim 1, wherein the measurement module comprises at least:
the device comprises a photoelectric conversion unit, an AD sampling unit, a digital phase meter and an angle resolving unit;
a photoelectric conversion unit configured to convert a beat signal into an electric signal;
an AD sampling unit configured to convert an electric signal output from the photoelectric conversion unit into a digital signal;
a digital phase meter configured to calculate phase information of a reference beam and a measuring beam from the digital signal;
and the angle calculating unit is configured to calculate the included angle between the measuring beam and the reference beam according to the phase information.
5. The wide-range high-precision differential wavefront sensing measurement device of claim 4, wherein the measurement module further comprises:
the adjustable gain control unit and the anti-aliasing filtering unit are arranged between the photoelectric conversion unit and the digital phase meter.
6. The wide-range high-precision differential wavefront sensing measurement device of claim 1, further comprising a collimation module disposed between the laser source and the first beam splitter group for collimating a reference beam incident on the first beam splitter group.
7. The device of claim 6, wherein the collimating module comprises a polarization maintaining fiber and a collimating lens, and the reference beam is incident on the first beam splitter group through the polarization maintaining fiber and then through the collimating lens along the propagation direction of the light.
8. The wide-range high-precision differential wavefront sensing measurement device of claim 6, further comprising an acousto-optic frequency shifter disposed between the laser source and the collimation module.
9. The wide-range high-precision differential wavefront sensing measurement device of claim 1, further comprising a second beam splitter group disposed behind the laser source and configured to split the laser light emitted by the laser source into at least two reference beams of equal intensity.
10. The wide-range high-precision differential wavefront sensing measurement device of claim 1, wherein the measuring beam is formed by reflecting laser light emitted from a laser source through a second beam splitter group.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117537937A (en) * | 2024-01-05 | 2024-02-09 | 国科大杭州高等研究院 | Direction control system for inhibiting nonlinearity of differential wavefront sensing technology |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117537937A (en) * | 2024-01-05 | 2024-02-09 | 国科大杭州高等研究院 | Direction control system for inhibiting nonlinearity of differential wavefront sensing technology |
| CN117537937B (en) * | 2024-01-05 | 2024-04-16 | 国科大杭州高等研究院 | Direction control system for inhibiting nonlinearity of differential wavefront sensing technology |
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