New method to diagnose spatial laser beam parameters

Transcription

1 INDLAS 2013, LID-LBC Symposium, Bran, 05/22/13 New method to diagnose spatial laser beam parameters G. Nemeş 1,2, A.Stratan 1, A. Zorilă 1,3, Ioana Dumitrache 1,3, L. Rusen 1, L. Neagu 1 1 ISOTEST Laboratory, NILPRP, 409 Atomiştilor Str., Măgurele - Bucharest, Romania 2 ASTiGMAT TM, 3409 Pecky Cedar Ct., Sacramento, CA 95827, USA; gnemes98@hotmail.com 3 "Politehnica" University of Bucharest, 313 Splaiul Independenţei, Bucharest, Romania

2 Acknowledgments - Sponsors: POS CCE "Investments for your future" Ministry of National Education, Romania - Co-sponsor: European Fund for Regional Development (EFRD/FEDR) - Invited guests - supporting LID-LBC mini-symposium - "Horia Hulubei" NIPNE/IFIN, Magurele - Bucharest - sponsoring invited guests - Audience - interest Official project number and title: Project POS CCE No. 172 / 2010 "Facility for laser beam diagnosis and ISO characterization / certification of behavior of optical components/materials subjected to high power laser beams / ISOTEST"

3 OUTLINE 1. Introduction 2. VariSpot TM 3. Experiments 4. Results and discussion 5. Conclusion

4 1. Introduction Goal: Measuring laser beam spatial parameters ISO ,2,3 Classical method Laser + focusing spherical lens + longitudinally translating camera Can we find other methods?

5 Basic concepts Types of beams (geometrical classification, ISO ,2,3) ST, ASA, RSA, GA Parameters of interest for: ASA beam ST beam Waist size(s): w 0x, w 0y ; D 0x, D 0y w 0 ; D 0 Waist location(s): z 0x, z 0y z 0 Beam divergence(s): θ x, θ y θ Rayleigh length(s): z Rx, z Ry z R Beam propagation ratio(s): M 2 x, M 2 y M 2 Methods to measure laser beam spatial parameters - Classical: Spherical lens and longitudinal (z axis) movement - New: Cylindrical optics and rotational (angular) movement VariSpot TM ASTiGMAT

6 2. VariSpot TM VariSpot TM = New family of zoom optical systems rotating cylindrical lenses Originally developed for material processing and medical applications

7 VariSpot TM principle - simplest example 2 - lens system: + Cylindrical lens, cylindrical axis fixed, vertical (f, 0) + Cylindrical lens, cylindrical axis rotatable about z (f, β) y x z Waist D 0 β (f, 0) (f, β) α = 90 0 β Detector (target) plane Round spot D(α) Incoming beam d 1 (>0) d 20 (>0)

8 Examples: VariSpot TM systems for R&D FS UV-VIS-NIR FS

9 Examples: VariSpot TM systems FL VIS (demo unit) FS UV-VIS-NIR (R&D unit) FS (industrial unit)

10 VariSpot TM to characterize spatial beam parameters Theory ("In theory, there should be no difference between theory and practice, but in practice, there is") Free-space D(z) VariSpot TM D(α) D 0 D m D(z) = D 0 [1 + (z - z 0 ) 2 /z R2 ] 1/2 D(α) = D m {1 + [sin(α) - sin(α 0 )] 2 /r 2 } 1/2 Equivalence: D(z) D(α); z sin(α); D 0 D m ; z R r; z 0 sin(α 0 )

11 VariSpot TM to characterize spatial beam parameters Theory: input-output relations (thin lens) d 20 - distance after VariSpot, where the spot is round d 1 - distance from incoming beam waist plane to VariSpot TM first lens α = 90 0 β - control parameter D 0 - incoming beam waist diameter θ - incoming beam divergence (full angle) z R - incoming beam Rayleigh length D(α) - diameter of the round spot at target (CCD camera) plane D m - minimum round spot diameter at target plane d 20 = f(z 2 R + d 12 )/(z 2 R + d 2 1 d 1 f) d 1 = f(1 f/d 20 )/[(1 f/d 20 ) 2 + r 2 ] D(α) = D m {1 + [sin(α) sin(α 0 )] 2 /r 2 } 1/2 z R = fr/[(1 f/d 20 ) 2 + r 2 ] D m = D 0 d 20 /[d 1 (1 + z R2 /d 12 ) 1/2 ] D 0 = D m f/{d 20 [(1 f/d 20 ) 2 + r 2 ] 1/2 } r = (fz R )/(z 2 R + d 12 ) M 2 = (π/4)fd m2 /(λrd 202 ) θ = D m [(1 f/d 20 ) 2 + r 2 ] 1/2 /(rd 20 )

12 Method of measuring beam parameters using VariSpot TM Find and measure d 20 by locating the round spot after VariSpot TM Measure D(α) at the appropriate target plane (at d 20 ) for different α Include D m, the "angular near-field", and the "angular far-field" for α Similarity to ISO standard for near-field and far-field Fit D(α) and determine α 0, D m, r D(α) = D m {1 + [sin(α) sin(α 0 )] 2 /r 2 } 1/2 Recover by calculations the original beam parameters

13 Precautions at using VariSpot TM Distance d 20 for the round spot after VariSpot TM is slightly different than the distance to the waist plane d 2w for a lens with same f, d 20 d 2w Spot profile in the waist plane, at d 2w, after VariSpot TM α = 0 0 α = 10 0 D 20 = mm Spot profile in the plane of round spot, at d 20, after VariSpot TM α = 0 0 α = 20 0 D m = mm > D 20

14 3. Experiments Three configurations Configuration 1: Classical method, spherical lens + moving camera Configuration 2: Classical method, VariSpot TM as spherical lens (α = 0 0 ) Configuration 3: New method, Varispot TM as rotating optics, get D(α) at d 20

15 4. Results and discussions 0,7 0,6 0,5 Equation D4s D4s Hyperbolic fit of D4s y = ((M*Zr* )*(1+((x-Z0)/Zr)^2))^(0.5) Value Standard Error M 1, ,01005 Z0 398, ,35613 Zr 28, ,32979 D4s (mm) 0,4 0,3 0,2 0,1 Configuration 1 0, z from lens (mm) Propagation after lens ("image beam") Parameter Value Rel. error (%) M D 01 (mm) z R1 (mm) θ 1 (mrad) Recovered original beam parameters ("object beam") z 01 (mm)

16 Results and discussions 0,8 0,7 0,6 0,5 Equation D4s D4s Hyperbolic fit of D4s y = ((M*Zr* )*(1+((x-Z0)/Zr)^2))^(0.5 ) Value Standard Error M 1, ,02052 Z0 344,4438 0,52528 Zr 23, ,51946 D4s (mm) 0,4 0,3 0,2 0,1 Configuration 2 0, z from lens (mm) Propagation after VariSpot TM as spherical lens lens ("image beam") Parameter Value Rel. error (%) M D 01 (mm) z R1 (mm) Recovered original beam parameters ("object beam") θ 1 (mrad) z 01 (mm)

17 Results and discussions 1,4 1,2 1,0 Equation D4sx D4sx diagnoza_eq_propag_varispot (User) Fit of Book1 D4sx y = Dm*(1+((x-s0)/r)^2)^(1/2) Value Standard Error Dm 0, ,00366 s0-0, r 0, ,00147 D α (mm) 0,8 0,6 0,4 0,2 0,0-0,2-0,1 0,0 0,1 0,2 0,3 0,4 sin (α) Configuration 3 D(α) after VariSpot TM, in target plane, at d 20 Parameter Value Rel. error (%) M D 01 (mm) z R1 (mm) Recovered original beam parameters ("object beam") θ 1 (mrad) z 01 (mm)

18 Experiments - Configuration 3. Corrections Corrections for thick optical system: f Cyl = 302 mm VariSpot TM as a spherical lens for α = 0 0, finding its corrected effective focal length, f C - Measuring: He-Ne laser + 4x BE + VariSpot TM finding waist position d 2w = f C = 300 mm - Data calculated for f C = 300 mm and for f C = 299 mm Better results for f C = 299 mm Parameter Lens, f = 338 mm VariSpot TM, f C = 300 mm α = 0º VariSpot TM, f C = 300 mm Variable α M ± 2 % 1.18 ± 4 % 1.18 ± 6 % D 01 (mm) 0.82 ± 5 % 0.89 ± 6 % 0.86 ± 6 % z R1 (mm) 726 ± 10 % 834 ±11 % 773 ± 12 % θ 1 (mrad) 1.13 ± 5 % 1.07 ± 6 % 1.11± 7 % z 01 (mm) 1895 ± 9 % 1887 ± 11 % 1916 ± 13 % Parameter Lens, f = 338 mm VariSpot TM, f C = 299 mm α = 0º VariSpot TM, f C = 299 mm Variable α M ± 6 % D 01 (mm) ± 6 % z R1 (mm) ± 11 % θ 1 (mrad) ± 7 % z 01 (mm) ± 13 %

19 6. Conclusion - Demonstrated new method to measure spatial beam parameters - Uses rotating cylindrical optics, fixed CCD camera position (one translation only) - "Propagation" formulae analogue to classical method (free-space propagation) - ISO recommendations (near-field, far-field measurements) have a straightforward analogue and can easily be implemented - Reasonable small relative errors ( 15 %) for preliminary measurements - Needs more work on corrections - Needs more experiments - Needs detailed error propagation analysis - Needs extension/experiments to measure ASA beams (theory does exist)