Analysis and Suppression of Crosstalk Stray Light in a Microlens Array Scanning and Searching System - MDPI
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micromachines Article Analysis and Suppression of Crosstalk Stray Light in a Microlens Array Scanning and Searching System Zhiyang Lv, Yunhan Huang and Zhiying Liu * School of Opto-Electronic Engineering, Key Laboratory of Optoelectronic Measurement and Optical Information Transmission Technology of Ministry of Education, Changchun University of Science and Technology, Changchun 130000, China * Correspondence: lzycccccc@126.com Abstract: The microlens array (MLA) system can aid in realizing fast beam deflection owing to the lateral displacement between arrays. The MLA system has the advantages of miniaturization and good functionality. However, during system operation, crosstalk beams are generated between each microlens array unit, introducing additional stray light, thus affecting the imaging contrast of the system. Therefore, this study uses the matrix operation method to trace the paraxial ray to trace the optical system and analyzes the generation mechanism of crosstalk stray light in the MLA system. Furthermore, this study proposes a crosstalk suppression method based on a stop array to reasonably suppress stray light. Finally, an example of an infrared array scanning infrared optical system is considered so as to verify the correctness and feasibility of the proposed crosstalk stray light suppression method. Therefore, this paper introduces the stray light suppression principle to guide the optical design process of the system, providing a theoretical basis for the design and analysis of the microlens array scanning and search system. Keywords: microlens array; beam crosstalk; stop array; stray light; optical simulation 1. Introduction Citation: Lv, Z.; Huang, Y.; Liu, Z. The microlens array is widely used in optical imaging detection, laser radar, satellite Analysis and Suppression of remote sensing, and military fields because of its low beam-pointing deviation, high Crosstalk Stray Light in a Microlens scanning rate, and rapid steering during dynamic imaging [1,2]. Array Scanning and Searching The processing technology of microlens is also developing with the demand. In 2016, System. Micromachines 2023, 14, 336. researchers presented a method for preparing well-defined microlenses based on polymer https://doi.org/10.3390/ phase separation in the presence of supercritical carbon dioxide (scCO2). Microlenses mi14020336 with dimensions from 2 to 15 µm and contact angles from 55◦ to 112◦ were successfully Academic Editor: Jaeyoun Kim obtained through adjustment of the kinetic conditions and outgassing rate, affording great promise for applications in bioimaging, photolithography, light harvesting, and optical Received: 15 December 2022 nanosensing [3]. In 2019, researchers proposed a manufacturing technique named laser Revised: 11 January 2023 catapulting (LCP), which enables the preparation of microlenses with controlled geometry Accepted: 20 January 2023 and curvature. Arrays of circular, triangular, and cylindrical microlenses with a radius Published: 28 January 2023 between 50–250 µm and 100% fill-factor can. Be obtained [4]. In 2021, a highly integrated planar annular microelectrode array was proposed to achieve an electrowetting tunable MLA. The planar microelectrode was fabricated by electrohydrodynamic jet (E-jet) printing Copyright: © 2023 by the authors. and the liquid microlens was then deposited in situ on the microelectrode. This method Licensee MDPI, Basel, Switzerland. can be beneficial for cell imaging, optofluidic systems, and microfluidic chips [5]. This article is an open access article Several studies have been conducted in these areas. The University of Konstanz in Ger- distributed under the terms and many developed a micro-opto-electro-mechanical multiplexer system for fast imaging [6]. conditions of the Creative Commons The University of Tokyo in Japan used piezoelectric ceramics to drive microlens arrays Attribution (CC BY) license (https:// for beam scanning [7]. The Huazhong University of Science and Technology combined creativecommons.org/licenses/by/ microlens array and convergent lens for beam deflection [8]. Tianjin University designed a 4.0/). microlens array system by integrating the transmitter and receiver for continuous scanning Micromachines 2023, 14, 336. https://doi.org/10.3390/mi14020336 https://www.mdpi.com/journal/micromachines
Micromachines 2022, 14, x 2 of 14 Micromachines 2023, 14, 336 2 of 14 microlens array and convergent lens for beam deflection [8]. Tianjin University designed a microlens array system by integrating the transmitter and receiver for continuous scan- ning imaging [9]. However, with increasing the scanning angle, beam crosstalk occurs imaging between [9]. the However, microlens with arrayincreasing units; thatthe is, scanning angle, beam light is incident on thecrosstalk adjacent occurs between lens units, in- the microlens array units; that is, light is incident on the adjacent terfering with the normal light transmission as stray light, thus reducing the imaging qual- lens units, interfering with ity ofthe the normal system. light transmission as stray light, thus reducing the imaging quality of the system. Several solutions have been proposed to solve the problem of crosstalk between lenses.Several In 1993,solutions Watsonhave beencrosstalk-free realized proposed to solve the problem and large fill factorofbeam crosstalk between control lenses. by adding In 1993, Watson realized crosstalk-free and large fill factor beam microlens arrays that function as field mirrors, effectively expanding the radial displace- control by adding microlens arrays ment and thatimproving function asthe field mirrors, scanning effectively field of view expanding [10]. In 2004, theresearchers radial displacement designed the and improving the scanning field of view [10]. In 2004, researchers second array as a double-sided lens array that consists of the objective and collimating designed the second array as lensa double-sided arrays on thelens same array that consists substrate, so thatofthe thefirst objective side ofand thecollimating second rowlens canarrays be used onasthe same substrate, so that the first side of the second row can the field mirror, and they can move in the same manner; furthermore, a certain amount of be used as the field mirror, and they can move eccentricity in the exists samegenerating without manner; furthermore, stray light [11]. a certain However, amount of eccentricity it is necessary exists to ensure without generating stray light [11]. However, it is necessary that the front surface of the second array contains the image point of the first array. In to ensure that the front surface of theasecond 2018, array laboratory in contains the image Beijing proposed an point imaging of the methodfirst combining array. In 2018, a laboratory microlens and stopin Beijing arrays, proposed enabling the an imaging microlensmethod array tocombining image in the microlens staring andfieldstop arrays, of view enabling with a limitedthe microlens array to image in the staring field of view with a limited object distance. The stop array was used to eliminate crosstalk and to achieve low-distor- object distance. The stop array was used tion imaging to eliminate [12]. However,crosstalk it was limitedand totoachieve microlens low-distortion array imaging imaging in the[12]. However, staring field itofwas limited to microlens view with limited far object distance. array imaging in the staring field of view with limited far objectTherefore, distance. in this study, the system model with a moving front group and a fixed Therefore, rear group in thistostudy, is selected realizethe thesystem imaging model of thewith a moving microlens arrayfront in the group swingand a fixed scanning rear group is selected to realize the imaging of the microlens array field of view at an infinite object distance; that is, the light from the off-axis object point is in the swing scanning field of view converted intoat parallel an infinite object light throughdistance; that is, thearray the microlens lighttofrom the off-axis achieve object point beam scanning. Theis converted matrix formula into parallel of paraxial lightraythrough tracing is the microlens used to describe arraythetosource achieve beam scanning. of crosstalk The stray light matrix formula of paraxial ray tracing is used to describe the in the MLA system, and the stray light is eliminated as the stop can block the propagation source of crosstalk stray light in of the MLA light. Thesystem, and theare design results stray light is based simulated eliminated on theassystem the stop can block the performance propagation parameters to of verify the correctness of the theory, realize high contrast and high definition imaging ofto light. The design results are simulated based on the system performance parameters verify the correctness the system, and guarantee of theatheory, reliablerealize designhigh andcontrast processing andofhigh the definition MLA system. imaging of the system, and guarantee a reliable design and processing of the MLA system. 2. Generation Mechanism of Crosstalk Stray Light 2. Generation Mechanism of Crosstalk Stray Light The scanning function of the MLA system is realized as a result of the mutual dis- The scanning function of the MLA system is realized as a result of the mutual displace- placement between the front and rear microlens arrays. With increasing the swing angle, ment between the front and rear microlens arrays. With increasing the swing angle, the the light light thatthat should should have have beenbeen emitted emitted fromfrom array array lenslens unit unit 1 enters 1 enters unit10 ,1' unit and, and some some of of the the light may reach the adjacent array lens unit0 2 ' , interfering with the light may reach the adjacent array lens unit 2 , interfering with the normal beam imaging normal beam im- aging of of the lens the array arrayunit, lensthus unit,reaching thus reaching the image the image planeplane without without following following the specified the specified path. path. At theAtsamethe time, samethis time, this part ofpart lightofcauses light causes light light loss lossarray of the of thelens array lens unit 10 , unit 1' , and and thus light thus light cannot fill the MLA aperture, cannot fill the MLA aperture, as shown in Figure 1. as shown in Figure 1. Array 1 Array 2 Unit 1 Unit 1' Unit 2 Unit 2' Figure 1. Figure 1. Schematic of the MLA MLA system system crosstalk crosstalkstray straylight. light. The scanning function of the microlens array is realized owing to mutual displacement, and the light transmission for different swing angles corresponds to the varying stray light distribution. For the convenience of discussion, we select two microlens symmetrical arrangements with identical positive power for analysis. Figure 2 shows a schematic of a
Micromachines 2022, 14, x 3 of 14 The scanning function of the microlens array is realized owing to mutual displace- Micromachines 2023, 14, 336 3 of 14 ment, and the light transmission for different swing angles corresponds to the varying stray light distribution. For the convenience of discussion, we select two microlens sym- metrical arrangements with identical positive power for analysis. Figure 2 shows a sche- single of matic microlens a single system constructed microlens using two positive system constructed lenses. using two At this positive time,At lenses. it isthis a zero field time, it ofaview, is zero that fieldis, ofthe twothat view, lenses have is, the nolenses two relative displacement. have no relative displacement. L1 DL De L2 Figure 2. Schematic Schematic of of zero zero field-of-view field-of-view of of aa single singlegroup groupmicrolens microlenssystem. system. The entrance entrance pupilpupil of of the the system systemisisdefined definedas De,which asDe, whichisissmaller smallerthan thanitsitsarray arraylens lens aperture D DLL..When Whenlightlightenters entersthe thefull fullaperture, aperture,thetheblue bluearea arearepresents representsthe theimaging imaginglight, light, the green and the green area area represents represents the the light light that that has has still still not not passed passedthe thecorresponding correspondingarray array aperture; this aperture; this light light inin the the green greenarea area isis defined definedas asType Type 11 stray straylight. light.The Theapertures aperturesofofthe the light line in the green area above above and and below below De De are are LL11and andLL22, ,respectively. respectively. When the When the field field angle angle gradually graduallyincreases, increases,thethedisplacement displacementdistancedistancebetween betweenthe thetwo two positive power components of the corresponding MLA system positive power components of the corresponding MLA system is Δ. The red area repre- is ∆. The red area represents the light sents entering the light the adjacent entering the adjacent array aperture, array andand aperture, its incident its incident aperture apertureis defined is defined asasL3 . Normal imaging light from other units is superimposed to form L3. Normal imaging light from other units is superimposed to form an image together on an image together on the image the imageplane, reducing plane, reducing thetheimaging imaging quality; quality;this thisisisdefined definedas asType Type 22 stray light. At stray light. Atthis this time, Type time, Type 11 stray stray light light below below De Deisisrelatively relativelyreduced, reduced,but butititdoes doesnot notdisappear, disappear,asasshown shown in Figure in Figure 3.3. L3 Ray1 L1 Ray2 De P0 Δ L2 Ray2 Ray1 L4 Figure Figure 3. 3. Schematic Schematic of of MLA MLA system systemat atany anyswing swingangle. angle. When the When the field field angle angle continues continues to to increase increaseto tothe themaximum, maximum,the thelower loweredge edgeofofthe the Micromachines 2022, 14, x 4 of 14 imaging light imaging light reaches reaches the the lower lower side side of ofthe the microlens microlensunit, unit,Type Type11stray straylight lightunder under DeDe disappears, and gradually disappears, and Type Type 2 stray light gradually gradually increases, increases, as as shown shown inin Figure Figure 4. 4. L3 L1 Ray1 Ray2 De Δ Ray2 Ray1 Figure 4. Schematic Schematic of of the the MLA MLA system system at at the the maximum maximumswing swingangle. angle. 3. Theoretical Analysis of Crosstalk Stray Light This section analyzes the light transmission of the MLA system at any swing angle, as shown in Figure 3. Expressions for various beam apertures (1)–(3) are derived from the
Micromachines 2023, 14, 336 4 of 14 Figure 4. Schematic of the MLA system at the maximum swing angle. 3. Theoretical Analysis of Crosstalk Stray Light 3. Theoretical Analysis This section analyzesofthe Crosstalk Stray Lightof the MLA system at any swing angle, as light transmission shown This section 3. in Figure analyzes the light Expressions for transmission various beamofapertures the MLA(1)–(3) systemare at derived any swing fromangle, the as shown inofFigure perspective 3. Expressions geometric for various optics, where P0 is thebeam apertures intersection (1)–(3) of the mainareray derived of the from the imaging perspective ray of geometric and the first surface. Atoptics, where the same the time, is schematic the intersection of the of the main system ray of the parameters imag- is shown ingFigures in ray and the first 3 and 5. surface. At the same time, the schematic of the system parameters is shown in Figures 3 and 5. D De L1 = L − , (1) 2 2 = − , (1) D De L2 = L + ( P0 − ), (2) =2 + ( −2 ), (2) DL DL L3 = − ( P0 + ) = −P . (3) 2= − ( +2 ) = − 0. (3) Figure 5. Schematic Figure 5. Schematic of of MLA MLA system system parameters. parameters. Here, fov, Here, fov, n L ,, INA, INA, and and ββrepresent representthe theangle angleofof view, view, refractive refractive index index of MLA of MLA sys- system tem material, numerical aperture angle between positive power components, material, numerical aperture angle between positive power components, and ratio of the and ra- tio of the back intercept of the power component to the thickness of the back intercept of the power component to the thickness of the lens, respectively. By con-lens, respec- tively. structingBythe constructing relationship thebetween relationship between the the parameters, theparameters, the system system parameter parameter expressions (4)– expressions (4)–(6) can be obtained according to the derivation presented a previous re- (6) can be obtained according to the derivation presented a previous report [13]. is the port [13]. td is the central thickness of the microlens and B is a coefficient less than 1. central thickness of the microlens and B is a coefficient less than 1. D ·td∙ , , e ==B (4) (4) ∙ ∙ f ov· B·t ∆ =Δ = ∙ d ,, (5) (5) 2· I N A ∙ ∙ ∙ ∙ 2·n = · β· I N A2 + f ovm∙· X ∙ . (6) L ∙ ∙ ∙ DL = · B · t d . (6) 2· n · β · I N A2 The ordinate value of is obtainedLby reverse tracking, as follows: The ordinate value of P0 is obtained by ∙ reverse ∙( ∙ tracking, ∙ )∙ as follows: =− , (7) ∙ ∙ B· f ov·( B·n L − 2· I N A)·td where = ∙ − 2 ∙ , P and −m in the formula 0 =fov , the maximum field of view.(7) 4I N A2 ·n Lrepresents ·β The system can be well described by these basic composition parameters. X = B·n L −Formulas whereSubstituting 2· I N A, and fovminto (4)–(6) in the formula(1)–(3), Formulas represents we obtain the maximum field of view. the following The system can be well described by these basic composition parameters. Substituting Formulas (4)–(6) into Formulas (1)–(3), we obtain the following B· f ovm · X ·td L1 = , (8) 4I N A2 ·n L · β B·( f ov − f ovm )·( B·n L − 2· I N A)·td L2 = − , (9) 4I N A2 ·n L · β B· f ov· X ·td L3 = , (10) 4I N A2 ·n L · β Subsequently, we define the upper and lower edge rays of Type 2 stray light in Figure 4 as Ray 1 and Ray 2, respectively, and trace the rays to obtain the propagation law of Type 2 stray light.
∙ ∙ ∙( )∙( ∙ ∙ )∙ =− , (9) ∙ ∙ ∙ ∙ ∙ = , (10) ∙ ∙ Micromachines 2023, 14, 336 5 of 14 Subsequently, we define the upper and lower edge rays of Type 2 stray light in Figure 4 as Ray 1 and Ray 2, respectively, and trace the rays to obtain the propagation law of Type 2 stray light. We Wediscuss discussthetheray raytracing tracingmatrix matrixrepresenting representingthe thesystem systemfrom fromthethepoint pointof of incidence incidence to to the the point of exit. exit. gives gives the the propagation propagation pathpath dia- diagram of light gram of light in ainsingle a single lens lens [14], [14], as as shown shown in in Figure Figure 6. 6. Figure6. Figure 6. Propagation Propagationpath pathdiagram diagramof oflight lightin insingle singlelens. lens. Then, the propagation from point AA00 through the optical system consisting of two Then, the propagation from point through the optical system consisting of two refractive surfaces to A3 can be described by Equation (11). A3 refractive surfaces " tot2 # " can be described # " by Equation #" (11). # " # 1 0 1 nt10 1 0 1 nt00 x3 1 n0 x0 = 2 · 1n2 0 −n2 0 · 1 · 10 0· · (11) n3 · β 3 1 0 1 −′ −R 2 1 10 1 − n1′R−− n1 1 01 1 n0 · β 0 ∙β = ′ ∙ − ∙ ′ ∙ − ∙ ∙ ∙β (11) 1 1 1 Micromachines 2022, 14, x 0 1 0 1 0 1 6 of 14 Therefore, the microlens array system in this study uses three steps to track, as shown in Figure 7. Therefore, the microlens array system in this study uses three steps to track, as shown in Figure 7. Ray1 Step1 -fov h1 na u1 r2 nL r1 nL Δ h2 r1 r2 u2· nL h3 Step2 u3 Step3 Figure7.7.Schematic Figure Schematicofofthe theray-tracing ray-tracingsteps stepsofofthe thearray arraysystem. system. Step 1. The matrix is used to trace the light path to the primary image plane. The ray tracing matrix equation is expressed as follows: 1 0 1 0 ℎ1 1 1 [ ]=[ ] ∙ [ − 1] ∙ [ ] ∙ [ − 1] ∙ [ 2 ] (12) ∙ 1 0 1 2 0 1 1 − Step 2. Trace the optical path from the primary image plane to the inner side of Lens
Micromachines 2023, 14, 336 6 of 14 Step 1. The matrix is used to trace the light path to the primary image plane. The ray tracing matrix equation is expressed as follows: " #" #" #" # 1 ntba 1 ntdL DL h1 1 0 1 0 = · n L −n a · · n a −n L · 2 (12) n a · u1 0 1 r2 1 0 1 r1 1 − f ov Step 2. Trace the optical path from the primary image plane to the inner side of Lens 2. The ray tracing matrix equation is expressed as follows: " #" # 1 ntba h2 1 0 0 = n a −n L · · (13) n L · u2 −r2 1 0 1 n a · u1 Step 3. Trace the optical path from the inside to the outside of Lens 2. The ray tracing matrix equation is expressed as follows: " #" # 1 ntdL h3 1 0 D + h2 = n L −n a · · L (14) n a · u3 −r1 1 0 1 n L · u2 The exit angle u3 and height h3 of the ray after passing through the array system can be obtained as: ( B − 2I N A· β)· f ovm · X + 2· I N A2 ·n L · β u3 = − , (15) 2· I N A2 · β 2· I N A2 ·n L · β − ( f ov − f ovm )· X h3 = · B·td . (16) 4· I N A2 · n L · β Similarly, we can obtain the propagation results of Ray 2 as: ( B − 2I N A· β)· f ovm · X + 2· I N A2 ·n L · β u4 = − , (17) 2· I N A2 · β f ovm · X + 2· I N A2 ·n L · β D h4 = 2 · B·td = L . (18) 4· I N A · n L · β 2 The exit aperture of Ray 2 can be defined by h4−h3, as shown in Formula (19): B· f ov·td · X L4 = . (19) 4· I N A2 · n L · β It can be observed that the sizes of L4 and L3 tend to be the same, and the values of u4 and u3 tend to be the same; that is, the angle of the outgoing light of the array system is approximately parallel. This provides an idea for the suppression and elimination of this type of stray light. Therefore, we can select the basic composition parameters of the system to change the system shape, thereby inhibiting the formation of this type of stray light. 4. Design of Crosstalk Stray Light Suppression The generation and theoretical analysis of crosstalk stray light indicate that an optiaml aperture should be selected to effectively suppress stray light. It is assumed that the lenses of the MLA system are symmetrically arranged about the primary image plane with equal power, the central light is parallel to the optical axis at the primary image plane, and the MLA system is usually combined with the infrared optical system for imaging. Therefore, the MLA system has an aperture stop array at the exit pupil, as shown in Figure 8.
The generation and theoretical analysis of crosstalk stray light indicate that an op- tiaml aperture should be selected to effectively suppress stray light. It is assumed that the lenses of the MLA system are symmetrically arranged about the primary image plane with equal power, the central light is parallel to the optical axis at the primary image plane, and the MLA system is usually combined with the infrared Micromachines 2023, 14, 336 optical system for imaging. Therefore, the MLA system has an aperture stop array 7atofthe 14 exit pupil, as shown in Figure 8. Figure8.8.Schematic Figure Schematicof ofthe theray-tracing ray-tracingof ofthe thearray arraysystem. system. The The pupillary distancetstp pupillary exit distance tstpcan canbebe obtained obtained byby ray-tracing ray-tracing thethe positive positive power power lens lens behind behind the the primary primary image image plane, plane, as as shown shown ininFormula Formula(20). (20).ToTo suppress suppress stray light, light, aa double doublestopstoparray arraygroup groupisisset. set.AsAsshown shown ininFigure Figure8, 8, TypeType1 stray light 1 stray cancan light be eliminated be eliminatedby setting an aperture stop array; that is, the aperture stop array not only by setting an aperture stop array; that is, the aperture stop array not only acts as an exit acts as an exit pupil in the system, pupil but alsobut in the system, aids in restricting also some stray aids in restricting some light from stray participating light in imaging. from participating By in im- observing the propagation path of the crosstalk stray light, it is found aging. By observing the propagation path of the crosstalk stray light, it is found that re- that residual Type 2sidual stray Type light still interferes 2 stray with light still imaging. interferes Therefore, with imaging.we can effectively Therefore, we cansuppress Type effectively sup-2 stray light by setting crosstalk suppression stop array and coating press Type 2 stray light by setting crosstalk suppression stop array and coating the ab- the absorption film at any position sorption filmbetween the primary at any position imagethe between plane and the primary frontplane image surface andof the the second array of front surface of the microlenses. the second array of the microlenses. ( B·n − 2I N A) L tstp = ( ∙ 2 ) · B·td . (20) 4I = N A ·n L · β ∙ ∙ . (20) ∙ ∙ Figure 9 is a schematic of the stop placement of an array system, and Figure 10 Figure illustrates 9 is a schematic a special of the case of stray stop light placement shown suppression of an array system, in Figure and 9. At Figure this time,10 illus- owing trates a special case of stray light suppression shown in Figure 9. At to the reasonable setting of various parameters of the system, Types 1 and 2 stray lightthis time, owing to the reasonable setting of various parameters of the system, Types 1 and do not need to be set with the crosstalk suppression stop array, but can be independently 2 stray light do not need toby suppressed bethe set aperture with the stop crosstalk array.suppression P1 and P2 are stop array, as defined butthe can be independently highest and lowest suppressed by the aperture stop array. P 1 and P2 are defined as the highest and lowest positions of Ray 2 on the exit pupil plane, respectively. P3 and P4 are the upper and lower positions edge of Ray positions of 2the onstop the exit at thepupil exit plane, respectively. pupil position, P3 and P4The respectively. are expression the upper and lower is shown edge positions in Formula (21). of the stop at the exit pupil position, respectively. The expression is shown in Formula (21). P1 : −tstp , h4 , P2 : −tstp , h3 , P3 : 0, − De 2 + N · DL , ( N = 0, ±1, ±2 . . . . . .) . (21) Micromachines 2022, 14, x 8 of 14 P4 : 0, − DL + De + N · DL , ( N = 0, ±1, ±2 . . . . . .) 2 Crosstalk suppression stop Aperture stop tstp Figure 9. Schematic Figure9. Schematic of of the the stop stop placement placementof ofan anarray arraysystem. system. P1 P2 h3 h4 Upper marginal line Lower
Micromachines 2023, 14, 336 tstp 8 of 14
Figure 9. Schematic of the stop placement of an array system.
P1
P2 h3 h4
Upper
marginal line
Lower
marginal line P3
tstp P4
Figure10.
Figure 10.Specific
Specificschematic
schematicof
ofthe
thestray
straylight
lightsuppression.
suppression.
Based on Formula (21), we can obtain
1the
: (− upper and lower edge angles as follows:
, ℎ4 ),
2 : (− , ℎ3 ),
4 ·( N − 1)· I N A2 ·n · β (21)
U pper = (2N − 1)· f ov +− 2 + ∙ ), ( = 0,L±1,,±2.
3 :m(0, ( N. .=. . .0,) ±.1, ±2 . . . . . .), (22)
X
{ 4 : (0, − + 2
+ ∙ ), ( = 0, ±1, ±2. . . . . . )
4·( N − 1)· I N A2 ·n L · β
Lower = ( 2N − 3 )· f ov m +
Based on Formula (21), we can obtain the , ( N = 0, ±1, ±2 . . . . . .). (23)
X upper and lower edge angles as follows:
2 ∙ ∙
Combining Formulas
= (2 (22),
− 1)(23), and+(15),
∙ we obtain
4∙( −1)∙
, ( = 0, ±1, ±2. . . . . . ), (22)
2· I N A2 ·n L · β·[( B−2I N A· β)· X +4· I N A2 ·( N −1)· β] 2· I N A2 ·n L · β·[( B4−∙2I(
N A·−
β)·1) 2 N −1)· β]
I N A2 ·(
X +4∙ ·
f ovm ≈ − , −3) ∙ ∙ ∙ , ( N
2 . . ..). .. . . ). (24)
X ·[( B−2I N A· β)· X +4· I N
A2 ·( N +1=)· β(2
] − B−+
X ·[(
= 0,±
= 0, 1, ±±2.
±1,
2I N A· β)· X +4· I N A2 ·( N −3)· β] , ( (23)
When the fovFormulas
Combining m value meets the above
(22), (23), and (15),parameter
we obtainrequirements, it can ensure that the
Type 2 stray light is always shielded by the aperture stop array.
2∙ 2 ∙ ∙ ∙[( −2 ∙ )∙ +4∙ 2 ∙( −1)∙ ] 2∙ 2 ∙ ∙ ∙[( −2 ∙ )∙ +4∙ 2 ∙( −1)∙ ]
≈ [− We discuss 2
the distribution
, − of Type 1 and 2 stray light at the], exit
( =pupil
0, ±1, position
±2. . . ).in this (24)
∙[( −2 ∙ )∙ +4∙ ∙( +1)∙ ] ∙[( −2 ∙ )∙ +4∙ 2 ∙( −3)∙ ]
section. Figure 11 shows the influence of fovm parameter changes on the distribution of
stray When the fovm them,
light. Among value meets
Type 1the above
stray light,parameter
shown inrequirements,
green, can beiteliminated
can ensurethrough that the
Type
the 2 straystop
aperture lightarray.
is always shielded
The white, red,byand theblack
aperture
areasstop array. the exit ray region, Type
represent
2 strayWe discuss
light, and the outside
distribution
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Typesystem,
1 and 2respectively.
stray light atWhen
the exit
thepupil
red line positionreaches in
thisblack
the section. Figure
area, Type 11 shows
2 stray the is
light influence
emitted of fovm parameter
outside the array changes on the the
system. When distribution
red line
of stray light.
coincides withAmong
the greenthem, Type
area, Type1 stray
2 stray light, shown
light in part
in this green, can
can bebe eliminatedtogether
suppressed through
the aperture
through stop array.
the aperture The
stop white,
array. red, and
When the black
red lineareas represent
coincides thethe
with exitwhite
ray region,
area, Type Type
22 stray
stray light
light,in
and this
thepart enters
outside of the array
subsequentsystem, system throughWhen
respectively. the exit
the pupil
red line aperture,
reaches
causing
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area, Type The design
2 stray light is aims to make
emitted Typethe
outside 2 stray light
array exit the
system. Whensystem theas farline
red as
possible, or make it coincident with Type 1 stray light and be suppressed
coincides with the green area, Type 2 stray light in this part can be suppressed together by the aperture
stop arraythe
through together.
aperture stop array. When the red line coincides with the white area, Type 2
It can be observed from Figure 11a that when the maximum field of view, that is, fovm ,
value changes, the aperture range of the system changes, and the aperture range is directly
proportional to the fovm value. At the same time, we observe that the fovm value has a
negligible effect on the change in Type 2 stray light.
It can be observed from Figure 11b that when the B value changes, the aperture range
of the system changes, and the aperture range is directly proportional to the B value. At
the same time, we observe that the B value has a significant effect on the change in Type 2
stray light. By increasing the B value, Type 2 stray light can be emitted at a larger angle,
almost to the outside of the system.stray light in this part enters the subsequent system through the exit pupil aperture, caus- ing adverse effects. The design aims to make Type 2 stray light exit the system as far as Micromachines 2023, 14, 336 9 of 14 possible, or make it coincident with Type 1 stray light and be suppressed by the aperture stop array together. Exit ray region Exit ray region fovm(°) B Exit pupil plane Exit pupil plane (a) (b) Exit ray region Exit ray region fov(°) INA Exit pupil plane Exit pupil plane (c) (d) Exit ray region β Exit pupil plane (e) Figure11. Figure 11. Different Different plots plots on onthe theexit exitpupil pupilplane. plane. (a) (a)Plot Plotbetween betweenfovfovmm and and the the exit exitpupil pupilplane plane (where fov = fovm, B = 0.1333, nL = 4.025, INA = 3.3438°,◦β = 0.5333, td = 3.0). (b) Plot between B and the (where fov = fovm , B = 0.1333, nL = 4.025, INA = 3.3438 , β = 0.5333, td = 3.0). (b) Plot between B and exit pupil plane (where fovm = 3°, nL = 4.025, INA = 3.3438°, β = 0.5333, td = 3.0). (c) Plot between fov the exit pupil plane (where fovm = 3◦ , nL = 4.025, INA = 3.3438◦ , β = 0.5333, td = 3.0). (c) Plot between and the exit pupil plane (where fovm = 3°, B = 0.13333, nL = 4.025, INA = 3.3438°, β = 0.5333, td = 3.0). fov and the exit pupil plane (where fovm = 3◦ , B = 0.13333, nL = 4.025, INA = 3.3438◦ , β = 0.5333, (d) Plot between INA and the exit pupil plane (where fovm = 3°, B = 0.13333, nL = 4.025, β =0.5333, td = t3.0). d = 3.0). (d) between (e) Plot β andINA Plot between andpupil the exit the exit pupil plane plane (where (where fovm fovm = 3◦ , B = 3°, B=0.13333, nL== 0.13333, 4.025, INA nL==3.3438°, 4.025, βtd=0.5333, t = 3.0). (e) Plot between β and the exit pupil plane (where fovm = 3 ◦ , B=0.13333, = 3.0). d nL = 4.025, INA = 3.3438◦ , td = 3.0). It can be observed from Figure 11a that when the maximum field of view, that is, fovm, valueFigure 11c the changes, shows the relationship aperture range of the between fov andand system changes, thethe exitaperture pupil plane. It directly range is can be observed proportional to the fovm value. At the same time, we observe that the fovm value has aType that a reasonable basic composition parameter of the system can ensure that neg- 2 stray light in the system always lies in the area of Type 1 stray light at the exit pupil plane. ligible effect on the change in Type 2 stray light. Finally, Type 2 stray light can be eliminated through a separate aperture stop array. It can be observed from Figure 11b that when the B value changes, the aperture range It can be observed from Figure 11d that when the numerical value of INA changes, of the system changes, and the aperture range is directly proportional to the B value. At the aperture range of the system changes significantly, and the aperture range is inversely the same time, we observe that the B value has a significant effect on the change in Type proportional to the numerical value of INA. By reducing the INA value, Type 2 stray light 2 stray light. By increasing the B value, Type 2 stray light can be emitted at a larger angle, can be emitted at a larger angle, and can be emitted to the outside of the system. almost to the outside of the system. It can be observed from Figure 11e that when the value of β changes, the aperture Figure 11c shows the relationship between fov and the exit pupil plane. It can be ob- range of the system changes significantly, and the aperture range is inversely proportional served that a reasonable basic composition parameter of the system can ensure that Type to the β value. By decreasing the β value, Type 2 stray light can be emitted at a larger angle, and this stray light can be emitted to the outside of the system. We can observe that increasing the B value, decreasing the INA value, or decreasing the β value can realize a large exit angle, allowing Type 2 stray light to exit the system directly. At the same time, the system design parameters can be appropriately selected
Micromachines 2023, 14, 336 10 of 14 so that Type 2 stray light whose exit range is still in the system always coincides with the area of Type 1 stray light, and the system crosstalk stray light can be effectively suppressed through the aperture stop array. Thus, this design aims to reduce the influence of stray light as much as possible without additional stops, and to provide guidance for the subsequent system simulation. 5. Instance System Verification Considering a specific infrared band microlens array scanning system as an example, the presented theory is validated. See Table 1 for detailed parameters of the system. Table 1. Array system parameters. Parameter Value Array size 13.5 mm × 13.5 mm Number 9×9 Single lens size 1.5 mm × 1.5 mm Layer 2 Central wavelength 4 µm Lens shape rectangle n n1 = n2 = 4.025058 Swinging angle δ 4◦ × 4◦ The optical system is constructed according to the above parameters to obtain the corresponding arrangement of two rows of 9 × 9 microlens arrays. An aperture stop array is placed at the exit pupil. The optical engineering simulation software FRED is used to simulate the crosstalk of the microlens array with only aperture stop array and no crosstalk Micromachines 2022, 14, x 11 of 15 suppression stop array when the microlens array is staggered along the Y axis and the swing angle is −2◦ , as shown in Figure 12. (a) Schematic of crosstalk beams in the system (b) Partial enlarged view (red arrows: crosstalk beams ) Figure12. Figure 12.FRED FREDsimulation simulationof ofcrosstalk crosstalkphenomenon phenomenonininthe themicrolens microlensarray. array. Toobserve To observe thethe crosstalk crosstalk phenomenon phenomenon clearly, clearly, FREDFRED is usedistoused to simulate simulate a small a small amount amount of obliqueofparallel obliquebeams parallel beamsthrough passing passingthethrough the microlens microlens array system, arrayandsystem, and two two identical microlens arrays are arrays identical microlens symmetrically arranged toarranged are symmetrically form a telescope to form system to ensure a telescope systemparallel to en- beam emission, sure parallel and emission, beam we set theand lightwe source energy set the light to 1 W. It source can betoobserved energy 1 W. It canfrom beFigure observed12 that from when the12 Figure system has only that when the an aperture system stop array, has only the crosstalk an aperture beams stop array, thementioned in the crosstalk beams theoretical mentionedanalysis do exist inanalysis in the theoretical the light dotransmission process exist in the light of the system transmission andof process continue the sys- to tempropagate through and continue the aperture to propagate stopthe through array to interfere aperture withtoimaging. stop array interfere Aswiththe lenses imaging. are As arranged the lenses in arean array, the arranged crosstalk in an beams array, the generated crosstalk beamsby each lensbyunit generated eachare arranged lens unit are arranged at the same angle, and they exit periodically, and the image power distribution is shown in Figure 13a.
To observe the crosstalk phenomenon clearly, FRED is used to simulate a small amount of oblique parallel beams passing through the microlens array system, and two identical microlens arrays are symmetrically arranged to form a telescope system to en- sure parallel beam emission, and we set the light source energy to 1 W. It can be observed from Figure 12 that when the system has only an aperture stop array, the crosstalk beams Micromachines 2023, 14, 336 11 of 14 mentioned in the theoretical analysis do exist in the light transmission process of the sys- tem and continue to propagate through the aperture stop array to interfere with imaging. As the lenses are arranged in an array, the crosstalk beams generated by each lens unit are at the sameatangle, arranged andangle, the same they exit andperiodically, and the image they exit periodically, power and the distribution image is shown power distribution in Figure 13a. is shown in Figure 13a. (a) Y axis, δ = −2° (b) Y axis, δ = 2° (c) X axis, δ = −2° (d) X axis, δ = 2° Figure13. Figure 13.Imaging Imagingdiagrams diagrams under under several several characteristic characteristic situations. situations. Theabove The abovesimulation simulation shows shows the the crosstalk crosstalk of the array when it moves relative to the YYaxis axis and −2◦When and δ == −2°. . When thethe image image plane is atisdifferent plane positions, at different the number positions, of lines the number with of lines energy with aliasing energy will be aliasing willdifferent. At the be different. Atsame time,time, the same because the microlens because arrayarray the microlens is a two- is a dimensional dynamic two-dimensional scanning, dynamic lightlight scanning, maymay enter fromfrom enter any any direction, andand direction, crosstalk willwill crosstalk oc- cur at different positions of the array. As shown in Figure occur at different positions of the array. As shown in Figure 13, image power13, image power distributions onthe on theplane planeunder underseveral severalcharacteristic characteristic situations situations are are given. given. Wetake We takethe axis,δδ==− theYYaxis, 2◦ as −2° as an an example. example. As Asthe thenormal normal imaging imaging beam beam and and crosstalk crosstalk beam beam propagate propagate on thethe image imageplaneplanethrough throughthe theaperture aperture stop stop array array andand distribute distribute at at in- intervals, respectively;atatthis tervals, respectively; thistime, time,we weadjust adjustthetheposition positionof ofthe the image image plane plane so so that that the crosstalk crosstalk beam beam can can be be clearly clearly observed. observed. We use FRED to perform advanced advanced ray ray tracing, tracing, and andthe thebeams beamsgenerate generate power power separately separately on on the the image plane image and separate plane from from and separate each other, each as shown in Figure 13a. Table 2 shows the power values of each aperture in Figure 13a. Table 2. Power value (Watts) of each aperture (Y axis, δ = −2◦ ). 1 2 3 4 5 6 7 8 9 1 0.005319 0.005183 0.005211 0.005183 0.005319 0.005183 0.005211 0.005183 0.005319 2 0.004894 0.004762 0.004774 0.004762 0.004894 0.004762 0.004774 0.004762 0.004894 3 0.004623 0.004487 0.004487 0.004487 0.004623 0.004487 0.004487 0.004487 0.004623 4 0.004487 0.004355 0.004355 0.004355 0.004486 0.004355 0.004355 0.004355 0.004487 5 0.004487 0.004355 0.004355 0.004355 0.004486 0.004355 0.004355 0.004355 0.004487 6 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 7 0.004623 0.004487 0.004487 0.004487 0.004623 0.004487 0.004487 0.004487 0.004623 8 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 9 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 From the data in Table 2 and Figure 13, it can be observed that the 9 × 9 microlens array system has crosstalk beams superimposed on normal beams, that is, images and energy superimposed on the first and second lines of the array interfere with normal beam imaging. Therefore, we place a crosstalk suppression stop array at a distance of 0.2 mm
7 0.004623 0.004487 0.004487 0.004487 0.004623 0.004487 0.004487 0.004487 0.004623 8 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 9 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 Micromachines 2023, 14, 336 From the data in Table 2 and Figure 13, it can be observed that the 9 × 9 microlens 12 of 14 array system has crosstalk beams superimposed on normal beams, that is, images and energy superimposed on the first and second lines of the array interfere with normal beam imaging. Therefore, we place a crosstalk suppression stop array at a distance of 0.2 mm from the front surface of the second row of microlens arrays to avoid crosstalk beams from the front surface of the second row of microlens arrays to avoid crosstalk beams interfering with imaging in the system. Figure 14 illustrates the simulation of the imaging interfering with imaging in the system. Figure 14 illustrates the simulation of the imaging of the system after adding the crosstalk suppression stop array. of the system after adding the crosstalk suppression stop array. (a) Schematic of non-crosstalk beams in the system (b) Image power distribution on the plane Figure14. Figure 14.Imaging Imagingdiagram diagramwith witha acrosstalk crosstalksuppression suppressionstop stoparray array(Y(Yaxis, axis,δ δ= =−−2°). 2◦ ). Thepower The power values values of each of each aperture aperture are given are given according according to 14, to Figure Figure 14, asinshown as shown Table 3.in Table 3. Table 3. Power value (Watts) of each aperture with crosstalk suppression stop array (Y axis, δ = −2◦ ). Table 3. Power value (Watts) of each aperture with crosstalk suppression stop array (Y axis, δ = −2°). 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 2 1 0.0044870.004487 0.004355 0.004355 0.004355 0.004355 0.004355 0.004355 0.004487 0.004487 0.004355 0.004355 0.004355 0.004355 0.0043550.004487 0.004355 0.004487 3 2 0.0046230.004487 0.004355 0.004487 0.004355 0.004487 0.004355 0.004487 0.004487 0.004623 0.004355 0.004487 0.004355 0.004487 0.0043550.004623 0.004487 0.004487 4 0.004487 0.004355 0.004355 0.004355 0.004486 0.004355 0.004355 0.004355 0.004487 5 0.004487 0.004355 0.004355 0.004355 0.004486 0.004355 0.004355 0.004355 0.004487 6 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 7 0.004623 0.004487 0.004487 0.004487 0.004623 0.004487 0.004487 0.004487 0.004623 8 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 9 0.004487 0.004355 0.004355 0.004355 0.004487 0.004355 0.004355 0.004355 0.004487 It can be observed from Figure 14a that there is no crosstalk beam generated after the crosstalk suppression stop array is placed. Figure 14b shows the image power distribution on the plane. The power in the first line of Figure 14b is generated by direct power of the light source, which can be eliminated by adjusting the size of the light source, and it is ignored. In addition, the power corresponding to each aperture is similar to that shown in Table 3, evenly distributed on the image plane, and the crosstalk beam has been effectively suppressed. By comparing the data in Tables 2 and 3, it can be seen that after the stop array is added, the power of the first and second rows of the array decreases. The reduced value is the crosstalk power superimposed on each aperture. Figure 15 plots the crosstalk power values of the two rows.
in Table 3, evenly distributed on the image plane, and the crosstalk beam has been effec- tively suppressed. By comparing the data in Tables 2 and 3, it can be seen that after the stop array is added, the power of the first and second rows of the array decreases. The reduced value is the crosstalk power superimposed on each aperture. Figure 15 plots the crosstalk power Micromachines 2023, 14, 336 13 of 14 values of the two rows. Figure 15. Diagram with crosstalk power values of the two rows (Y axis, δ = −2◦ ). Figure 15. Diagram with crosstalk power values of the two rows (Y axis, δ = −2°). As the crosstalk value in the second line is generated by the edge array, the crosstalk value the As crosstalk is reduced value in with compared the second the firstline is which line, generated makesby the the curves edge array, of thethe twocrosstalk lines have value is reduced compared with the first line, which makes the curves a certain distance. Increasing the size of the light source can reduce the distance. of the two lines have a certain distance. Therefore, Increasing the crosstalk the size ofstop suppression the array light source can be can reduce added the distance. according to the actual Therefore, situation the crosstalk to enable suppression the system to achieve stop array can be added interference-free accordingSimilarly, transmission. to the actual when situation to enable the relative the system displacement to achieve of the microlens interference-free array correspondstransmission. to differentSimilarly, whenthe swing angles, thecrosstalk relative suppression displacementstopof the microlens array array corresponds can also suppress to different the propagation of theswing angles, crosstalk beams. theIncrosstalk addition,suppression the method stop array crosstalk of adding can also suppression suppress thestoppropagation of the crosstalk arrays to eliminate crosstalk beams. can be Inextended addition,tothe themethod of adding array. M * N microlens crosstalk suppression stop arrays to eliminate crosstalk can be extended to the M * N microlens array. 6. Conclusions 6. Conclusions This study aimed to solve the basic problem of crosstalk generated by the microlens array Thissystem underto study aimed dynamic solve thescanning and toofclarify basic problem the generated crosstalk mechanism byand influence of the microlens crosstalk generation. Taking advantage of the characteristics of the array system under dynamic scanning and to clarify the mechanism and influence stop array thatofcan limit beam transmission, a design method of a double-stop array group was crosstalk generation. Taking advantage of the characteristics of the stop array that can proposed to beam limit suppress the crosstalk transmission, beams. a design We analyzed method the relationship of a double-stop between array group the structural was proposed to parameters of the microlens array and the position and size of the stop suppress the crosstalk beams. We analyzed the relationship between the structural array. The matrix pa- ray tracing rameters of themode was constructed microlens array and theto position completeand thesize system crosstalk of the strayThe stop array. light model matrix rayand realize the light control of different incident angles and eccentricity in dynamic scanning. Then, the stray light analysis software FRED was used to simulate an example of a system in different situations and to analyze its stray light suppression effect to verify the correctness of the theoretical model. Furthermore, the microlens array system can enlarge the dynamic scanning range without crosstalk, thus verifying the feasibility of the design method. In addition, it can aid in guiding the design and analysis of the microlens array scanning and searching system in the future. Author Contributions: Z.L. (Zhiyang Lv): conceptualization, investigation, methodology, simulation, validation, and writing original draft preparation; Z.L. (Zhiyang Lv) and Y.H.: theoretical analysis; Z.L. (Zhiying Liu): conceptualization, writing—review and editing, supervision, project administration, and funding acquisition. All authors have read and agreed to the published version of the manuscript. Funding: National Natural Science Foundation of China (61805025), and Jilin Scientific and Techno- logical Development Program (20200401055GX). Data Availability Statement: Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. Acknowledgments: The authors express their sincere thanks to the National Demonstration Center for Experimental Opto-Electronic Engineering Educations for their support with the experiments. Conflicts of Interest: The authors declare no conflict of interest.
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