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VARISPOT FS-100-1 BEHAVIOR IN COLLIMATED AND DIVERGING BEAMS: THEORY AND EXPERIMENTS

VARISPOT FS-100-1 BEHAVIOR IN COLLIMATED AND DIVERGING BEAMS: THEORY AND EXPERIMENTS. Liviu Neagu, Laser Department, NILPRP, Bucharest-Magurele, Romania lneagu@ifin.nipne.ro L. Rusen, M. Zamfirescu, Laser Department, NILPRP, Bucharest-Magurele, Romania

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VARISPOT FS-100-1 BEHAVIOR IN COLLIMATED AND DIVERGING BEAMS: THEORY AND EXPERIMENTS

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  1. VARISPOT FS-100-1 BEHAVIOR IN COLLIMATED AND DIVERGING BEAMS: THEORY AND EXPERIMENTS Liviu Neagu, Laser Department, NILPRP, Bucharest-Magurele, Romania lneagu@ifin.nipne.ro L. Rusen, M. Zamfirescu, Laser Department, NILPRP, Bucharest-Magurele, Romania George Nemeş, Astigmat, Santa Clara, CA, USA gnemes@astigmat-us.com

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

  3. 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

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

  5. Optical system: S A11 A12 B11 B12 A B A21 A22 B21 B22 S == C D C11 C12 D11 D12 C21 C22 D21 D22 • Properties: • 0 I 1 0 0 0 • S J ST = J ; J = ; J2 = - I; I = ; 0 = • - I 0 0 1 0 0 • ADT – BCT = I • ABT = BATdet S = 1; S - max. 10 independent elements • CDT = DCT • A, D elements: numbers • B elements: lengths (m) • C elements: reciprocal lengths (m-1) • Ray transfer property of S:Rout= S Rin

  6. Beam: P Beams in second - order moments: P = beam matrix <x2> <xy> <xu> <xv> <xy> <y2> <yu> <yv> W M W elements: lengths2 (m2) P = <RRT> = =;M elements: lengths (m) <xu> <yu> <u2> <uv> MT U U elements: angles2 (rad2) <xv> <yv> <uv> <v2> Properties: P > 0; PT= P  WT= W; UT= U; MT M  P - max. 10 independent elements Beam transfer property (beam "propagation" property) of S: Pout = S Pin ST W = W I Example of a beam (rotationally symmetric, stigmatic) and its "propagation" M = M I U = U I W= W0W2 = AATW0 + BBTU0 In waist: M = 0 ; Output M2 = ACT W0 + BDTU0 (z = 0) U = U0 plane: U2 = CCT W0 + DDTU0 Beam spatial parameters: D(z) = 4W1/2(z); q = 4U1/2 zR = W01/2/U1/2 = D0/q; M2= (p/4)D0q/l;

  7. (f, b) Waist D0 Target plane (f, 0) y b a= 900– b x Round spot D(a) z Incoming beam d1 (>0) d20 (>0) 3. VARISPOT Block diagram 2 - lens system: + Cylindrical lens, cylindrical axis fixed, vertical (f, 0) + Cylindrical lens, cylindrical axis rotatable about z (f, b)

  8. VariSpot input-output relations VariSpot and beam parameters d20 - working distance after VariSpot, where the spot is round d1 - distance from incoming beam waist plane to VariSpot first lens a = 900–b - control parameter D0 - incoming beam waist diameter q - incoming beam divergence (full angle) zR - incoming beam Rayleigh range D(a) - diameter of the round spot at target plane Dm - minimum round spot diameter at target plane DM - maximum round spot diameter at target plane 1: Simple and important cases 1a: Well collimated incoming beam: zR >> f; zR >> d1; d1 = irrelevant 1b: Diverging beam, incoming beam waist at VariSpot first lens: d1 = 0 2: General case Diverging incoming beam: d1 0

  9. VariSpot input-output relations 1. Well collimated incoming beam: zR >> f; zR >> d1 d20 = f D(a) = D0 [f2/zR2 + sin2(a)]1/2 = Dm [1 + sin2(a)/(f/zR)2]1/2 Dm = D(0) = D0 f/zR = qf DM = D(p/2) D0 KM = DM/Dm zR/f - dynamic range (zoom range) Compare D(a) = Dm [1 + sin2(a)/(f/zR)2]1/2 to free-space propagation: D(z) = D0 (1 + z2/zR2)1/2

  10. VariSpot input-output relations 2. General case: diverging incoming beam, d1 0 d20 = f(zR2 + d12)/(zR2 + d12 - d1f) D(a) = Dm {1 + sin2(a)/[(fzR)2/(zR2 + d12)2]}1/2 Dm = D(0) = D0 f (zR2 + d12)1/2/(zR2 + d12- d1f) DM = D(p/2) = D0 (zR2 + d12)1/2 [(zR2 + d12)2 + f2zR2]1/2/[zR(zR2 + d12- d1f)] KM = DM/Dm - dynamic range (zoom range) Compare D(a) = Dm {1 + sin2(a)/[(fzR)2/(zR2 + d12)2]}1/2 to free-space propagation: D(z) = D0 (1 + z2/zR2)1/2

  11. VariSpot input-output relations 2. General case: diverging incoming beam, d1 0 VARISPOT D(a) FREE SPACE D(z) Dm D0 Compare D(a) = Dm {1 + sin2(a)/[(fzR)2/(zR2 + d12)2]}1/2 to free-space propagation: D(z) = D0 (1 + z2/zR2)1/2

  12. Beam profiler (CMOS camera or scanning slits) VariSpot Beam expander or focusing lens He-Ne Laser d20 4. EXPERIMENTS Experimental setup

  13. Data on experiments CMOS camera beam profiler data(Type: WinCamD-UCM, Data Ray, USA) Pixel size: 6.7 mm 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: Dreal = 1.4 Ddisplayed Scanning slit beam profiler data (Type: BeamScan, Photon Inc., USA) Two orthogonal scanning slits Slit size: 1 mm x 3.4 mm VariSpot data (Type:FS -100 -1, Astigmat, USA) “FS”  focus-mode, short length; “100”  f = 100 mm; “1”  DM/D0 = 1 f= 100 mm a = 00 - 930 Manually rotatable mount; +/- 10 resolution

  14. Data on experiments Original He-Ne laser beam (l = 633 nm) Incoming beam data D0 = 0.83 mm zR = 780 mm M2 = 1.1 Collimated He-Ne laser beam after  4 x beam expander Incoming beam data Output results D0 = 3.3 mmDm theor = 40 mm; Dm exp = 73 mm zR = 8.5 m DM theor = 3.3 mm; DM exp = 3.4 mm (corr.) M2 = 1.6 d20 theor = d20 exp = 100 mm Diverging He-Ne laser beam after f0 = 300 mm spherical focusing lens Incoming beam data Output results D0 = 0.32 mmDm theor = 62 mm; Dm exp = 70 mm zR = 120 mm DM theor = 1.93 mm; DM exp = 2.0 mm M2 = 1.1 d20 theor = 119 mm; d20 exp = 122 mm VariSpot first lens placement from incoming beam waist: d1 = 600 mm

  15. For D(a) > 2.5 mm CMOS camera gives too small values due to low beam irradiance 5. RESULTS AND DISCUSSION Collimatedincoming beam: zR >> f; zR >> d1; (zR = 8500 mm; d1 = 0 mm; f = 100 mm) d20 = f D(a) = Dm [1 + sin2(a)/(f/zR)2]1/2 Dm = D0 f/zR DM = D0 DM theor = 3.3 mm measured on collimated beam DM exp = 3.4 mm from curve below D(a) = D0 sin(a)

  16. General case: diverging incoming beam, d1 0 (zR = 120 mm; d1 = 600 mm ; f = 100 mm) d20 = f(zR2 + d12)/(zR2 + d12 - d1f) D(a) = Dm {1 + sin2(a)/[(fzR)2/(zR2 + d12)2]}1/2 Dm = D0 f (zR2 + d12)1/2/(zR2 + d12- d1f) DM = D0 (zR2 + d12)1/2 [(zR2 + d12)2 + f2zR2]1/2/[zR(zR2 + d12- d1f)] D(a) = D0 sin(a)

  17. Examples of spots Incoming diverging beam, after 300 mm lens; d1 = 600 mm. D0 = 0.33 mm Beam profiler focusing lens He-Ne Laser d1

  18. Examples: VariSpot at working distance (WD) Incoming diverging beam; WD = d20 = 122 mm; a = - 10. D(a) = Dm = 74 mm VariSpot Beam profiler Beam expander He-Ne Laser d20

  19. Examples: VariSpot at working distance Incoming diverging beam; WD = d20 = 122 mm; a = 180 . D(a) = 0.6 mm VariSpot Beam profiler Beam expander He-Ne Laser d20

  20. Examples: VariSpot at working distance Incoming diverging beam; WD = d20 = 122 mm; a = 900. DM = 2.0 mm VariSpot Beam profiler Beam expander He-Ne Laser d20

  21. Discussion - Zoom range (K = DM/Dm) scales with zR/f in collimated beams: K = zR/f - Minimum spot size scales with f: Dm = D0f/zR = D0/K - Maximum spot size DM = D0 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

  22. Prototype Incoming beam Output beam Zoom factor (dynamic range) K = 7 : 1 Dm= 1 mm; DM= 7 mm

  23. 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 • Dm=70 mm; DM= 3.4 mm (collimated beam); K = (45-50):1 • Dm=70 mm; DM= 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

  24. Thank you for your attention!

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