CN101963492A - Displacement detecting device based on inner reflector of elliptic cylinder - Google Patents
Displacement detecting device based on inner reflector of elliptic cylinder Download PDFInfo
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Abstract
The invention discloses a displacement detecting device based on an inner reflector of an elliptic cylinder. In the device, a convex lens imaging principle is skillfully applied; the detection of the position of a light convergence point is converted into the detection of the most photosensitive point on an linear array photosensitive element by a photoluminescence substance (or a diffuse reflectance material), the inner reflector of the elliptic cylinder and the linear array photosensitive element; and the detection can be carried out only by a computer. The device comprises a point light source laser, a convex lens, the inner reflector of the elliptic cylinder and the linear array photosensitive element, wherein the point light source laser and the inner reflector of the elliptic cylinder are put on the same side of the convex lens; the photoluminescence substance (or the diffuse reflectance material) is coated on a focal line of the inner reflector of the elliptic cylinder; the focal line is superposed with an optical axis of the convex lens; and the linear array photosensitive element is put on the other focal line of the inner reflector of the elliptic cylinder for detecting the displacement of a surface to be detected. The device has the advantages of simple structure, convenient use and high measurement precision.
Description
Technical field
The present invention relates to the Photoelectric Detection field, use optical imaging concept to detect the non-contacting displacement detector of object under test relative displacement.
Background technology
Photoelectric detecting technology is a kind of new and high technology of non-cpntact measurement, it is carrier with the light signal, based on photoelectric device, by the light signal that is loaded with testee geometric sense or physical quantity is detected, analyzes, and obtain the geometric parameter of testee, promptly by the photoelectricity testing part receiving optical signals and be converted to electric signal, extract useful information by testing circuits such as input circuit, amplification filtering, again through A/D conversion interface input Computing, processing, parameters such as the geometric sense of demonstration or the required inspected object of printout or physical quantity at last.The present invention relates to optics, laser technology, precision optical machinery, electronics, multidisciplinary technical field such as photoelectric sense technology and computer technology, be light, machine,, calculate integrated detecting instrument and equipment, have high-speed, high precision, noncontact, be convenient to digitizing, being convenient to Computerized real-time data handles and controls, antijamming capability is strong, can realize characteristics such as online detection, can satisfy the needs of modern industry production development, its application almost can cover all manufacturing industry, application prospect is very wide, to improving the quality of products, enhance productivity, reduce labour intensity, it is significant to increase economic efficiency.
Along with the development of modern production and process technology, for the detection speed and the precision of processing parts higher requirement has been arranged, develop towards the direction of high-speed, high precision, noncontact and online detection.At present the noncontact displacement detection technique based on photoelectric detecting technology has been carried out big quantity research both at home and abroad.China Science ﹠ Technology University has proposed the optical fiber type displacement detecting technology based on CCD, the radiating portion of detection system is installed on the movement parts to be measured, detection system adopts Array CCD Camera to obtain tested optical fiber end outgoing hot spot gray distribution of image, extract the unique point of hot spot by the intensity-weighted method of average, obtain the displacement of optical fiber by the displacement of detected characteristics point, thereby obtain the displacement of measured piece, the stability of system is 1.5 μ m, system reaches the resolution of inferior pixel level (referring to " based on the optical fiber type displacement detecting technology of CCD ", Li Weimin, Yu Qiaoyun, Hu Hongzhuan etc.China Science ﹠ Technology University's journal, the 33rd volume, the 1st phase, 2003).Also have aviation aerospace institute of Nanjing Aero-Space University also to propose a kind of new method of utilizing light reflection principle to measure little displacement, utilize glass bead minute surface (minute surface is coated with and strengthens optical reflection coating) light reflection principle, when light shines on the spherical glass face along horizontal direction, incident light can reflect, at this moment, vertical movement about glass bead carries out
The time, can cause that the incident light incident angle changes, its reflected light reflection direction changes thereupon, so just, can utilize the difference of distance between incident light and the reflected light to carry out little displacement measurement, measuring accuracy is higher, realizes easily, cost is lower (referring to " a kind of new method of utilizing light reflection principle to measure little displacement ", Chen Renwen, Sun Yafei, Chen Yong; Spectroscopy and spectral analysis, the 24th volume, the 1st phase, 2004).
In above-mentioned two parts of documents, the former will be installed to transmitter on the object under test, and the latter will be fixed to glass bead on the object under test, and such metering system is inapplicable for a lot of situations.
Summary of the invention
Fundamental purpose of the present invention provides a kind of noncontact displacement pick-up unit based on the cylindroid internal reflector, and this device is simple to operate, the accuracy of detection height.
A kind of displacement detector based on the cylindroid internal reflector provided by the invention is characterized in that this device comprises pointolite laser instrument, convex lens, cylindroid internal reflector and linear array photo-sensitive cell;
Convex lens only leave photocentre photic zone and annular photic zone, and remainder scribbles light tight film;
The outside surface plating reflectance coating of cylindroid internal reflector, it is shaped as the oval cylinder of part amputation, section S is crossed second focal line of cylindroid internal reflector, this cross section is parallel to the minor axis B of cylindroid internal reflector, the first focal line place at the cylindroid internal reflector has the through hole that diameter is 0.2mm~0.5mm, scribbles photoluminescence material or diffuse-reflective material in the through hole;
The linear array photo-sensitive cell is bonded on the section S, and the light-sensitive surface of linear array photo-sensitive cell is pressed close to the cylindroid internal reflector, and it is parallel with the section S and first focal line, and make two focal line place plane symmetry of two outside surface P, Q and the cylindroid internal reflector of linear array photo-sensitive cell, make the sensitization element on the linear array photo-sensitive cell fully accept reflected light;
Cylindroid internal reflector and laser instrument are positioned at the same side of convex lens, the pointolite laser instrument is placed on the optical axis of convex lens, make its parallel light that sends in the optical axis of convex lens, scribble photoluminescence material or diffuse-reflective material on first focal line of cylindroid internal reflector, and first focal line overlaps with the primary optical axis of convex lens;
Laser instrument between convex lens and cylindroid internal reflector, pointolite laser front facet and convex lens should be apart from s according to the operating distance s of pointolite laser instrument
0Mean distance with object under test and convex lens
Determine that they satisfy
Relation;
If f is the focal length of convex lens, l is the distance of object under test and convex lens photocentre, and f and l satisfy f≤l≤2f;
Convergent point is meant the light of pointolite laser instrument emission, sees through the photocentre photic zone of convex lens, after the object under test diffuse reflection, sees through the convergent point of annular photic zone on the optical axis of convex lens.If l ' is the moving range of convergent point on the optical axis of convex lens, the length of linear array photo-sensitive cell at least should be greater than the maximum moving range 2~3mm of optical axis glazed thread convergent point, the length of cylindroid internal reflector equals the length of linear array photo-sensitive cell, and according to the scope of l ' determine the front end face of cylindroid internal reflector and convex lens photocentre apart from a
2, a
2Than l '
MinLittle 1~2mm, wherein l '
MinBe the minimum value in the moving range of convergent point on the optical axis of convex lens;
Being shaped as of pointolite laser instrument is cylindrical, and its diameter is d, and the distance of the rear end face of pointolite laser instrument and convex lens photocentre is a
1, the photocentre photic zone size of convex lens is 1.5mm~2.5mm for diameter, the width of annular photic zone is 1.5mm~2.5mm, the interior ring diameter d of the annular photic zone of convex lens
1Satisfy following relation:
Determine the outer shroud diameter d of the annular photic zone of convex lens according to the width of the annular photic zone of convex lens
2The outside diameter d of convex lens
3Outer shroud diameter d than annular photic zone
2Big 4~5mm;
The ratio of the length 2b of cylindroid internal reflector minor axis B and the length 2a of major axis A
Between, the length 2a of cylindroid internal reflector major axis A should satisfy:
L '
MaxBe the maximal value in the moving range of convergent point on the optical axis of convex lens, 2c is the distance of cylindroid internal reflector two focal lines.
The present invention utilizes pointolite laser instrument, convex lens, cylindroid internal reflector, photoluminescence material (or diffuse-reflective material) and linear array photo-sensitive cell to form the contactless displacement pick-up unit, the cylindroid internal reflector has two parallel focal lines, Tuo Yuan first focal line overlaps with the primary optical axis of convex lens in the present invention, and second focal line overlaps with the linear array photo-sensitive cell.This displacement pick-up unit has amplification to the displacement of object under test, to the displacement detecting precision height of object under test, and utilize body surface that the diffuse reflection of light is detected, need not touch object under test, it is little to can be used for range of movement, requires the high occasion of accuracy of detection.In a word, apparatus of the present invention can be carried out non-cpntact measurement to the relative displacement of examined object, and the measuring accuracy height is simple in structure, easy to operate.
Description of drawings
Fig. 1 is the index path of apparatus of the present invention;
Fig. 2 is the convex lens outside drawing of apparatus of the present invention, (2a) is front view, (2b) is left view;
Fig. 3 is cylindroid internal reflector, the photoluminescence material (or diffuse-reflective material) and line array CCD (or linear array DSP) structural drawing of apparatus of the present invention, (3a) be the sectional view of cylindroid internal reflector, (3b) be the cylindroid internal reflector stereographic map, (3c) be the manufacturing process of cylindroid internal reflector.
Fig. 4 is the cylindroid internal reflector index path of apparatus of the present invention;
Fig. 5 is the surface of intensity distribution on the linear array photo-sensitive cell of apparatus of the present invention.
Embodiment
In actual measurement, the light transmission convex lens photocentre photic zone that utilizes the pointolite laser instrument to send, project and form small light spot on the object under test surface and produce diffuse reflection, the annular photic zone of a part of light transmission convex lens after the diffuse reflection also converges at a bit on the optical axis (being cylindroid first focal line) of convex lens opposite side, at this moment the photoluminescence material at convergent point place (or diffuse-reflective material) sends the light of (reflection), by the cylindroid internal reflector light being converged at is equipped with on second focal line of linear array photo-sensitive cell, by detecting the variation of the position of light signal point of maximum intensity on the linear array photo-sensitive cell, can determine the displacement even the absolute position of object under test.If f is the focal length of convex lens, l is the distance of object under test and convex lens photocentre, and l ' is the convergent point of light on the optical axis of convex lens and the distance of convex lens photocentre, according to the geometric optical imaging formula
Have
When f≤l≤2f, this displacement pick-up unit to the enlargement factor of the displacement of object under test is
Because the displacement of the light convergent point of object under test and convex lens opposite side is non-linear relation, so the displacement of the light convergent point of convex lens opposite side is not directly proportional with the displacement of object under test, along with the mobile amplification multiple of object under test is also different, and this method has been ignored the refraction that takes place when light is injected cylindroid and has been waited other errors that manufacturing accuracy caused owing to principle and instrument, so the testing result of apparatus of the present invention can not be fully according to formula
Calculate, and should before use instrument be demarcated, to improve the accuracy of detection of instrument.
Below by by embodiment the present invention being described in further detail, but following examples only are illustrative, and protection scope of the present invention is not subjected to the restriction of these embodiment.
As shown in Figure 1, displacement detector of the present invention comprises pointolite laser instrument 1, convex lens 2, cylindroid internal reflector 3, photoluminescence material (or diffuse-reflective material) 13 and linear array photo-sensitive cell 14.
As shown in Figure 2,2 on convex lens leave photocentre photic zone 6 and apart from the annular photic zone 7 of photocentre certain distance, remainder is coated light tight film 15.Photocentre photic zone 6 sizes of convex lens 2 are 1.5mm~2.5mm for diameter, and the width of annular photic zone 7 is 1.5mm~2.5mm.
As shown in Figure 3, cylindroid internal reflector 3 is made for optical glass, its outside surface plating reflectance coating (as silver) 16, it is shaped as the oval cylinder (Fig. 3 b) of part amputation, described section S is crossed second focal line 12 of cylindroid internal reflector 3, this cross section is parallel to the minor axis B of cylindroid internal reflector 3, has the through hole that diameter is 0.2mm~0.5mm at first focal line, 11 places of cylindroid internal reflector 3, scribbles photoluminescence material (or diffuse-reflective material) 13 in the through hole.
Linear array photo-sensitive cell 14 is bonded on the section S, and the light-sensitive surface of linear array photo-sensitive cell 14 is pressed close to cylindroid internal reflector 3, and it is parallel with the section S and first focal line 11, and make two focal lines, 11, the 12 place plane symmetry of two outside surface P, Q and the cylindroid internal reflector of linear array photo-sensitive cell, make the sensitization element on the linear array photo-sensitive cell 14 fully accept reflected light.Linear array photo-sensitive cell 14 is line array CCD or linear array DSP.
Fig. 1 has expressed the assembly relation of each parts of displacement detector, cylindroid internal reflector 3 and pointolite laser instrument 1 are positioned at the same side of convex lens 2, pointolite laser instrument 1 is placed on the primary optical axis of convex lens 2, make its parallel light that sends in the primary optical axis of convex lens 2, and make each zone of the central transparent area 6 of convex lens all have laser to pass through as far as possible.Scribble photoluminescence material (or diffuse-reflective material) on last first focal line 11 of cylindroid internal reflector 3, and first focal line 11 should overlap with the primary optical axis of convex lens 2.
Pointolite laser instrument 1 is between convex lens 2 and cylindroid internal reflector 3, and pointolite laser instrument 1 front end face 5 should be according to the operating distance s0 of pointolite laser instrument 1 and the mean distance of object under test 4 and convex lens apart from s with convex lens 2
Determine that they satisfy
Relation.
According to the geometric optical imaging formula
Have
When f≤l≤2f, the enlargement factor of displacement is
Can determine the focal length of convex lens 2 according to the demand of displacement enlargement factor and the range of movement of object under test 4 (being the scope of l).When detecting distance at 1.2f≤l≤1.3f scope, this measurement mechanism can reach 11.11~25 times to the enlargement factor of displacement, and the average resolution rate can reach 0.5 μ m.
Pointolite laser instrument 1 profile is cylindrical, and its diameter is d, and the rear end face 20 of pointolite laser instrument 1 is a with the distance of convex lens 2 photocentres
1, object under test 4 is in moving process during in order to ensure detection, and light 8 is not blocked by the pointolite laser instrument, then the interior ring diameter d of the annular photic zone 7 of convex lens 2
1Should satisfy following relation:
Width according to convex lens 2 annular photic zones 7 is 1.5mm~2.5mm, can determine the outer shroud diameter d of the annular photic zone 7 of convex lens 2
2The outside diameter d of convex lens
3Outer shroud diameter d than annular photic zone 7
2Big 4~5mm.
In order to reduce the loss of light intensity after 3 internal reflections of cylindroid internal reflector as far as possible, promptly allow linear array photo-sensitive cell 14 can receive more rays, should guarantee the ratio of the length 2a of the length 2b of cylindroid internal reflector 3 minor axis B and major axis A
Between.Object under test 4 is in moving process when detecting, and light 8 is not blocked then by the outer cylinder T of cylindroid internal reflector 3 that the length 2a of cylindroid internal reflector 3 major axis A should satisfy:
(l '
MaxBe the maximal value in the moving range of convergent point 10 on the optical axis of convex lens 2,2c is the distance of 3 liang of focal lines of cylindroid internal reflector).
When making cylindroid internal reflector 3, adopt the semiellipse cylinder 17 and 18 of two outside surface plating reflectance coatings (as silver) 16, respectively on first focal line 11 of semiellipse cylinder 17 and 18, the semicolumn groove that to mark one diameter be 0.2mm~0.5mm is coated photoluminescence material (or diffuse-reflective material) 13 in the semicolumn groove; The part amputation of second focal line below 12 with semiellipse cylinder 17 and 18.And according to shown in Fig. 3 c, semiellipse cylinder 17,18 and linear array photo-sensitive cell 14 being bonded together with clear glass glue.
After light sends from pointolite laser instrument 1, the photocentre photic zone 6 of planoconvex lens 2 is incident upon on the examined object 4, through the annular photic zone 7 of some light transmission convex lens 2 after the diffuse reflection, and see through the end face 9 of cylindroid internal reflector, on the optical axis of convex lens 2, converge at a little 10; The light that photoluminescence material in this (or diffuse-reflective material) 13 (reflection) goes out after 3 reflections of cylindroid internal reflector, converges on second focal line 12 at linear array photo-sensitive cell 14 places, and the index path of cylindroid internal reflector 3 inside as shown in Figure 4.
Be the surface of intensity distribution of ray cast on linear array photo-sensitive cell 14 time as shown in Figure 5, as shown in Figure 1, the light scattering to all the winds that goes out from the photoluminescence material (or diffuse-reflective material) of the convergent point 10 of light 13 (reflection), but the light intensity that subpoint 19 places of convergent point 10 on linear array photo-sensitive cell 14 receive will be the strongest, so the light distribution on linear array photo-sensitive cell 14 will be the normal state form that the is similar to distribution that the center is narrowing toward each end broad in the middle to put 19, as shown in Figure 5.Because photoluminescence material (or diffuse-reflective material) 13 has certain diameter, so light is not to converge at a point on photoluminescence material (or diffuse-reflective material) 13, but has certain length, so as shown in Figure 5, the strongest place of light intensity neither a point, but certain-length is arranged, in the present invention with the mid point of light intensity peak position as the result who detects.
The process of using this displacement pick-up unit to carry out displacement detecting is:
(1) laser of launching from pointolite laser instrument 1, see through convex lens 2 photocentre photic zones 6, be incident upon on the examined object 4, through the annular photic zone 7 of some light transmission convex lens 2 after the diffuse reflection, and the end face 9 that passes cylindroid internal reflector 3 converges at a little 10;
(2) to all the winds send out (reflection) at the photoluminescence material (or diffuse-reflective material) 13 of light convergent point 10 and go out light, after the reflection of light through cylindroid internal reflector 3, converge on second focal line 12 that cylindroid internal reflector 3 is placed with linear array photo-sensitive cell 14;
(3) the linear array photo-sensitive cell 14, after light signal is converted into electric signal, is input in the computing machine and detects, the position at light intensity peak mid point place on the linear array photo-sensitive cell 14, projection on convex lens 2 optical axises is exactly the position of light convergent point 10 on convex lens 2 optical axises;
(4) according to the convex lens image-forming principle
When the changing of measuring point to be checked and convex lens 2 apart from l, convex lens opposite side light also can the changing of convergent point and convex lens 2 on convex lens 2 optical axises apart from l ', as long as know the focal length of convex lens, and measure the position l ' of light convergent point 10 on convex lens 2 optical axises with method noted earlier, just can calculate the position l of tested point, and then calculate the displacement l of tested point.For the refraction that reduces to take place when light is injected cylindroid waits other errors that manufacturing accuracy caused owing to principle and instrument, the position l of tested point can obtain according to position l ' and the result who before instrument is demarcated.
Example:
In this example, diffuse-reflective material---the Spectralon (R) of blue luxuriant and rich with fragrance optics (Labsphere), its diffuse reflectance is up to 96%-98% in employing.Pointolite laser instrument 1 is a semiconductor point light source laser instrument, and its diameter is φ 8mm, and long 20mm, operating distance 50mm, pointolite laser instrument 1 are apart from convex lens 12mm, and the rear end face 20 of pointolite laser instrument 1 is a with the distance of convex lens 2 photocentres
1=32mm; The focal distance f of convex lens is 30mm, and the diameter of photocentre transmission region is 2mm, and the interior ring diameter of annular photic zone is 16mm, and outer ring diameter is 20mm, and the convex lens external diameter is 25mm; The length 2a of cylindroid internal reflector major axis A is 24mm, and the length 2b of minor axis B is 16mm, and outside surface is silver-plated; Adopt TCD1501C type line array CCD, photosensitive pixel number is 5000, and pixel dimension is 7 μ m * 7 μ m * 7 μ m (adjacent picture elements centre distance), and this line array CCD one-dimensional image photosensitive region length is 35mm.Object under test is positioned over apart from convex lens 37mm~39mm scope, and measurement range is 2mm; The long 35mm of cylindroid internal reflector, the cylindroid internal reflector is positioned over apart from convex lens a
2=128mm place.During measurement, when object under test during apart from convex lens 2 photocentres 37mm~39mm, light distance of convergent point and convex lens in cylindroid internal reflector 3 is 130mm~158.6mm, enlargement factor is 11.11~18.36 times, because the resolution when CCD is detected is 1 pixel, pixel dimension is 7 μ m, so for the resolution of object under test be: 7 μ m/11.11 (doubly)~7 μ m/18.36 (doubly) ≈, 0.63 μ m~0.38 μ m.
Before use, should demarcate the displacement detector of the inventive method earlier, calibrate line array CCD (or linear array DSP) and go up the physical location of the pairing object under test of point of each pixel, the distance between the point of being demarcated is short more, and the measuring accuracy of displacement detector will be high more.When detecting, when convergent point not in the position of being demarcated, can carry out the position that interpolation obtains current object under test according to the physical location of the pairing object under test of being demarcated of point.In this example, selected each pixel is demarcated.
The above is one embodiment of the present of invention, but the present invention should not be confined to the disclosed content of this embodiment and accompanying drawing.So everyly do not break away from the equivalence of finishing under the spirit disclosed in this invention or revise, all fall into the scope of protection of the invention.
Claims (1)
1. the displacement detector based on the cylindroid internal reflector is characterized in that, this device comprises pointolite laser instrument (1), convex lens (2), cylindroid internal reflector (3) and linear array photo-sensitive cell (14);
Convex lens (2) only leave photocentre photic zone (6) and annular photic zone (7), and remainder scribbles light tight film;
The outside surface plating reflectance coating of cylindroid internal reflector (3), it is shaped as the oval cylinder of part amputation, section S is crossed second focal line (12) of cylindroid internal reflector (3), this cross section is parallel to the minor axis B of cylindroid internal reflector (3), locate to have the through hole that diameter is 0.2mm~0.5mm at first focal line (11) of cylindroid internal reflector (3), scribble photoluminescence material or diffuse-reflective material in the through hole;
Linear array photo-sensitive cell (14) is bonded on the section S, and the light-sensitive surface of linear array photo-sensitive cell (14) is pressed close to cylindroid internal reflector (3), and it is parallel with section S and first focal line (11), and make two focal lines (11), (12) place plane symmetry of two outside surface P, Q and the cylindroid internal reflector of linear array photo-sensitive cell, make the sensitization element on the linear array photo-sensitive cell (14) fully accept reflected light;
Cylindroid internal reflector (3) and laser instrument (1) are positioned at the same side of convex lens (2), pointolite laser instrument (1) is placed on the optical axis of convex lens (2), make its parallel light that sends in the optical axis of convex lens (2), scribble photoluminescence material or diffuse-reflective material on first focal line (11) of cylindroid internal reflector (3), and first focal line (11) overlaps with the primary optical axis of convex lens (2);
Laser instrument (1) is positioned between convex lens (2) and the cylindroid internal reflector (3), and pointolite laser instrument (1) front end face (5) should be according to the operating distance s of pointolite laser instrument (1) apart from s with convex lens (2)
0And the mean distance of object under test (4) and convex lens
Determine that they satisfy
Relation;
If f is the focal length of convex lens, l is the distance of object under test and convex lens photocentre, and f and l satisfy f≤l≤2f;
Convergent point (10) is meant the light of pointolite laser instrument (1) emission, sees through the photocentre photic zone (6) of convex lens (2), after object under test (4) diffuse reflection, sees through the convergent point of annular photic zone (7) on the optical axis of convex lens (2).If l ' is the moving range of convergent point (10) on the optical axis of convex lens (2), the length of linear array photo-sensitive cell (14) at least should be greater than the maximum moving range 2~3mm of optical axis glazed thread convergent point (10), the length of cylindroid internal reflector (3) equals the length of linear array photo-sensitive cell (14), and according to the scope of l ' determine the front end face of cylindroid internal reflector (3) and convex lens (2) photocentre apart from a
2, a
2Than l '
MinLittle 1~2mm, wherein l '
MinBe the minimum value in the moving range of convergent point (10) on the optical axis of convex lens (2);
Being shaped as of pointolite laser instrument (1) is cylindrical, and its diameter is d, and the distance of the rear end face of pointolite laser instrument (1) and convex lens (2) photocentre is a
1, photocentre photic zone (6) size of convex lens (2) is 1.5mm~2.5mm for diameter, the width of annular photic zone (7) is 1.5mm~2.5mm, the interior ring diameter d of the annular photic zone (7) of convex lens (2)
1Satisfy following relation:
Determine the outer shroud diameter d of the annular photic zone (7) of convex lens (2) according to the width of the annular photic zone (7) of convex lens
2The outside diameter d of convex lens
3Outer shroud diameter d than annular photic zone (7)
2Big 4~5mm;
The ratio of the length 2b of cylindroid internal reflector (3) minor axis B and the length 2a of major axis A
Between, the length 2a of cylindroid internal reflector (3) major axis A should satisfy:
L '
MaxBe the maximal value in the moving range of convergent point (10) on the optical axis of convex lens (2), 2c is the distance of cylindroid internal reflector (3) two focal lines.
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