VARISPOT FS BEHAVIOR IN COLLIMATED AND DIVERGING BEAMS: THEORY AND EXPERIMENTS Liviu Neagu, Laser Department, NILPRP, Bucharest-Magurele, Romania L. Rusen, M. Zamfirescu, Laser Department, NILPRP, Bucharest-Magurele, Romania George Nemeş, Astigmat, Santa Clara, CA, USA

OUTLINE 1. INTRODUCTION 2. OPTICAL SYSTEMS AND BEAMS – 4 x 4 MATRIX TREATMENT 3. VARISPOT 4. EXPERIMENTS 5. RESULTS AND DISCUSSION 6. CONCLUSION

1. INTRODUCTION Importance of variable spots at fixed working distance - Material processing Drilling, cutting - small spots Annealing, surface treatment - large spots - Biology, medicine (dermatology, ophthalmology) Destroying small areas of tissue Photo-treatment of large areas of tissue - Laser research Adjustable power/energy densities - laser damage research Obtaining variable spots at a certain target plane - Classical: Spherical optics and longitudinal movement - This work: Cylindrical optics and rotational movement  VariSpot

2. OPTICAL SYSTEMS AND BEAMS: 4 x 4 MATRIX TREATMENT Basic concepts: rays, optical systems, beams Ray: R R T = (x(z) y(z) u v)

Optical system: S A 11 A 12 B 11 B 12 A B A 21 A 22 B 21 B 22 S = = C D C 11 C 12 D 11 D 12 C 21 C 22 D 21 D 22 Properties: 0 I S J S T = J ; J = ; J 2 = - I; I = ; 0 = - I AD T – BC T = I AB T = BA T  det S = 1; S - max. 10 independent elements CD T = DC T A, D elements: numbers B elements: lengths (m) C elements: reciprocal lengths (m -1 ) Ray transfer property of S: R out = S R in

Beams in second - order moments: P = beam matrix W M W elements: lengths 2 (m 2 ) P = = = ; M elements: lengths (m) M T U U elements: angles 2 (rad 2 ) Properties: P > 0; P T = P  W T = W; U T = U; M T  M  P - max. 10 independent elements Beam transfer property (beam "propagation" property) of S: P out = S P in S T W = W I Example of a beam (rotationally symmetric, stigmatic) and its "propagation" M = M I U = U I W = W 0 W 2 = AA T W 0 + BB T U 0 In waist: M = 0 ; Output M 2 = AC T W 0 + BD T U 0 (z = 0) U = U 0 plane: U 2 = CC T W 0 + DD T U 0 Beam spatial parameters: D(z) = 4W 1/2 (z);  = 4U 1/2 z R = W 0 1/2 /U 1/2 = D 0 /  ; M 2 = (  /4)D 0  / ; Beam: P

Block diagram 2 - lens system: + Cylindrical lens, cylindrical axis fixed, vertical (f, 0) + Cylindrical lens, cylindrical axis rotatable about z (f,  ) 3. VARISPOT Round spot D(  ) Incoming beam y x z Waist D 0 Target plane d 1 (>0)d 20 (>0)  = 90 0 –   (f, 0) (f,  )

VariSpot and beam parameters d 20 - working distance after VariSpot, where the spot is round d 1 - distance from incoming beam waist plane to VariSpot first lens  = 90 0 –  - control parameter  D 0 - incoming beam waist diameter  - incoming beam divergence (full angle) z R - incoming beam Rayleigh range D(  ) - diameter of the round spot at target plane D m - minimum round spot diameter at target plane D M - maximum round spot diameter at target plane 1: Simple and important cases 1a: Well collimated incoming beam: z R >> f; z R >> d 1 ; d 1 = irrelevant 1b: Diverging beam, incoming beam waist at VariSpot first lens: d 1 = 0 2: General case Diverging incoming beam: d 1  0 VariSpot input-output relations

1. Well collimated incoming beam: z R >> f; z R >> d 1 d 20 = f D(  ) = D 0 [f 2 /z R 2 + sin 2 (  )] 1/2 = D m [1 + sin 2 (  )/(f/z R ) 2 ] 1/2 D m = D(0) = D 0 f/z R =   f D M = D(  2)  D 0 K M = D M /D m  z R /f - dynamic range (zoom range) Compare D(  ) = D m [1 + sin 2 (  )/(f/z R ) 2 ] 1/2 to free-space propagation: D(z) = D 0 (1 + z 2 /z R 2 ) 1/2

VariSpot input-output relations 2. General case: diverging incoming beam, d 1  0 d 20 = f(z R 2 + d 1 2 )/(z R 2 + d d 1 f) D(  ) = D m {1 + sin 2 (  )/[(fz R ) 2 /(z R 2 + d 1 2 ) 2 ]} 1/2 D m = D(0) = D 0 f (z R 2 + d 1 2 ) 1/2 /(z R 2 + d 1 2  d 1 f) D M = D(  2) = D 0 (z R 2 + d 1 2 ) 1/2 [(z R 2 + d 1 2 ) 2 + f 2 z R 2 ] 1/2 /[z R (z R 2 + d 1 2  d 1 f)] K M = D M /D m - dynamic range (zoom range) Compare D(  ) = D m {1 + sin 2 (  )/[(fz R ) 2 /(z R 2 + d 1 2 ) 2 ]} 1/2 to free-space propagation: D(z) = D 0 (1 + z 2 /z R 2 ) 1/2

VariSpot input-output relations 2. General case: diverging incoming beam, d 1  0 Compare D(  ) = D m {1 + sin 2 (  )/[(fz R ) 2 /(z R 2 + d 1 2 ) 2 ]} 1/2 to free-space propagation: D(z) = D 0 (1 + z 2 /z R 2 ) 1/2 D0D0 DmDm VARISPOT D(  ) FREE SPACE D(z)

4. EXPERIMENTS Experimental setup d 20 VariSpot Beam expander or focusing lens Beam profiler (CMOS camera or scanning slits) He-Ne Laser

Data on experiments CMOS camera beam profiler data (Type: WinCamD-UCM, Data Ray, USA) Pixel size: 6.7  m square Detector size: 1280 x 1024 pixels; 8.58 mm x 6.86 mm ADC dynamic range: 14 bits S/(rms)N: 500:1 Attenuator: gray glass, ND = 4.0 Note: Constant correction factor for CMOS camera: D real = 1.4 D displayed Scanning slit beam profiler data (Type: BeamScan, Photon Inc., USA) Two orthogonal scanning slits Slit size: 1  m x 3.4 mm VariSpot data (Type: FS , Astigmat, USA) “FS”  focus-mode, short length; “100”  f = 100 mm; “1”  D M /D 0 = 1 f = 100 mm  = Manually rotatable mount; +/- 1 0 resolution

Data on experiments Original He-Ne laser beam ( = 633 nm) Incoming beam data D 0 = 0.83 mm z R = 780 mm M 2 = 1.1 Collimated He-Ne laser beam after  4 x beam expander Incoming beam data Output results D 0 = 3.3 mm D m theor = 40  m; D m exp = 73  m z R = 8.5 m D M theor = 3.3 mm; D M exp = 3.4 mm (corr.) M 2 = 1.6 d 20 theor = d 20 exp = 100 mm Diverging He-Ne laser beam after f 0 = 300 mm spherical focusing lens Incoming beam data Output results D 0 = 0.32 mm D m theor = 62  m; D m exp = 70  m z R = 120 mm D M theor = 1.93 mm; D M exp = 2.0 mm M 2 = 1.1 d 20 theor = 119 mm; d 20 exp = 122 mm VariSpot first lens placement from incoming beam waist: d 1 = 600 mm

5. RESULTS AND DISCUSSION Collimated incoming beam: z R >> f; z R >> d 1 ; (z R = 8500 mm; d 1 = 0 mm; f = 100 mm) d 20 = f D(  ) = D m [1 + sin 2 (  )/(f/z R ) 2 ] 1/2 D m = D 0 f/z R D M = D 0 D M theor = 3.3 mm measured on collimated beam D M exp = 3.4 mm from curve below For D(  ) > 2.5 mm CMOS camera gives too small values due to low beam irradiance D(  ) = D 0 sin(  )

General case : diverging incoming beam, d 1  0 (z R = 120 mm; d 1 = 600 mm ; f = 100 mm) d 20 = f(z R 2 + d 1 2 )/(z R 2 + d d 1 f) D(  ) = D m {1 + sin 2 (  )/[(fz R ) 2 /(z R 2 + d 1 2 ) 2 ]} 1/2 D m = D 0 f (z R 2 + d 1 2 ) 1/2 /(z R 2 + d 1 2  d 1 f) D M = D 0 (z R 2 + d 1 2 ) 1/2 [(z R 2 + d 1 2 ) 2 + f 2 z R 2 ] 1/2 /[z R (z R 2 + d 1 2  d 1 f)] D(  ) = D 0 sin(  )

Examples of spots Incoming diverging beam, after 300 mm lens; d 1 = 600 mm. focusing lens Beam profiler He-Ne Laser D 0 = 0.33 mm d1d1

Examples: VariSpot at working distance (WD) Incoming diverging beam; WD = d 20 = 122 mm;  =  1 0. d 20 VariSpot Beam expander Beam profiler He-Ne Laser D(  ) = D m = 74  m

Examples: VariSpot at working distance Incoming diverging beam; WD = d 20 = 122 mm;  = D(  ) = 0.6 mm d 20 VariSpot Beam expander Beam profiler He-Ne Laser

Examples: VariSpot at working distance Incoming diverging beam; WD = d 20 = 122 mm;  = D M = 2.0 mm d 20 VariSpot Beam expander Beam profiler He-Ne Laser

Discussion - Zoom range (K = D M /D m ) scales with z R /f in collimated beams: K = z R /f - Minimum spot size scales with f: D m = D 0 f/z R = D 0 /K - Maximum spot size D M = D 0 for collimated beams - Minimum spots are larger due to cylindrical lens (circularity) aberrations - Errors to measure maximum spots due to insensitivity of CMOS camera and its fixed attenuator (too low power density) - Cheap, off the shelf lenses used, no AR coating for VariSpot

Prototype Zoom factor (dynamic range) K = 7 : 1 D m = 1 mm; D M = 7 mm Incoming beam Output beam

6. CONCLUSION New zoom principle demonstrated using rotating cylindrical lenses in collimated and diverging beam Experiments confirm the device theory High value of zoom factor (dynamic range of round spot sizes) for collimated incoming beam D m = 70  m; D M = 3.4 mm (collimated beam); K = (45-50):1 D m = 70  m; D M = 2.0 mm (diverging beam); K = (25-30):1 Low ellipticity round spots Minimum spot size limited by lens aberrations Improved results expected with good quality and AR coated cylindrical lenses

Thank you for your attention!