OPTICAL SYSTEM FOR VARIABLE RESIZING OF ROUND FLAT-TOP DISTRIBUTIONS George Nemeş, Astigmat, Santa...
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Transcript of OPTICAL SYSTEM FOR VARIABLE RESIZING OF ROUND FLAT-TOP DISTRIBUTIONS George Nemeş, Astigmat, Santa...
OPTICAL SYSTEM FOR VARIABLE RESIZING OF ROUND
FLAT-TOP DISTRIBUTIONS
George Nemeş, Astigmat, Santa Clara, CA, USA [email protected]
John A. Hoffnagle, IBM Almaden Research Center,
San Jose, CA, USA [email protected]
OUTLINE
1. INTRODUCTION
2. OPTICAL SYSTEMS AND BEAMS – MATRIX TREATMENT
3. VARIABLE SPOT RESIZING OPTICAL SYSTEM (VARISPOT)
4. EXPERIMENTS
5. RESULTS AND DISCUSSION
6. CONCLUSION
1. INTRODUCTION
• Importance of flat-top beams and spots
• Obtaining flat-top beams
- Directly in some lasers, at least in one transverse direction
(transverse multimode lasers; excimer)
- From other beams with near-gaussian profiles – beam shapers
(transverse single-mode lasers)
• Obtaining flat-top spots at a certain target plane
- Superimposing beamlets on that target plane (homogenizing)
- From flat-top beams by imaging and resizing this work
2. OPTICAL SYSTEMS AND BEAMS: MATRIX TREATMENT
Basic concepts: rays, optical systems, beams
Ray: R
RT = (x(z) y(z) u v)
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 0S J ST = J ; J = ; J2 = - I; I = ; 0 = - I 0 0 1 0 0
ADT – BCT = IABT = BAT det S = 1; S - max. 10 independent elementsCDT = DCT
A, D elements: numbers B elements: lengths (m)
C elements: reciprocal lengths (m-1)
Ray transfer property of S: Rout = S Rin
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 IExample of a beam (rotationally symmetric, stigmatic) and its "propagation" M = M I U = U I W = W0 W2 = AAT W0 + BBTU0
In waist: M = 0 ; Output M2 = ACT W0 + BDTU0 U = U0 plane: U2 = CCT W0 + DDTU0
Beam spatial parameters: D = 4W1/2; = 4U1/2; M2 = (/4)D0/; zR = D0/
Beam: P
Round spot D(α)
Quasi – Image Plane+ Cyl. (f, 0)
– Cyl. (–f, α)
Incoming beam
D0
y
x
z
Sph. f0
f0
Block diagram 3 - lens system: + cyl. lens, cyl. axis vertical ( f, 0) - cyl. lens, cyl. axis rotatable about z (-f, ) + sph. lens (f0) + free-space of length d = f0 (back-focal plane)
3. VARIABLE SPOT RESIZING OPTICAL SYSTEM(VariSpot)
W2 = W2 I; W2 = A2 W0 + B2 U0
W2() = [(f02/f2) sin2()] W0 + (f0
2) U0 = W0 [(f02/f2) sin2() + f0
2/z2R]
D() = D0 [(f02/f2) sin2() + f0
2/z2R]1/2 = Dm[1 + sin2()/sin2(R)]1/2
Compare to free-space propagation: D(z) = Dm[1 + z2/z2R]1/2
Dm = D2( = ) = D0 f0 / zR = f0
DM = D2( = 2) = D0 [(f02/f2) + f0
2/z2R]1/2 D0 f0/ f (for f/zR <<1)
sin(R) = f/zR; R = “angular Rayleigh range”
Perfect imager B = 0 W2 = A2 W0 beam-independent
“Image-mode” of optical system + incoming beam(beam-dependent - Rayleigh range zR): A2 W0 >> B2 U0 A2 >> B2/z2
R f/zR = sin(R) << sin() 1
VariSpot “image-mode” D() D0 (f0/f) sin()
VariSpot input-output relations
4. EXPERIMENTS
Experimental setup
Data on experiment
Incoming beam data ( = 514 nm) CCD camera data (type Dalsa D7)
- Gaussian beam Pixel size: 12 m
D0 = 4.480 mm Detector size: 1024 x 1024 pixels
= 0.154 mrad Dynamic range: 12 bits (4096 levels)
zR = 29.1 m Noise level: 2 levels
M2 = 1.05 Attenuator: Al film; OD 3
- Flat-top (Fermi-Dirac) beam
D0 = 6.822 mm
= 0.149 mrad
zR = 45.8 m
M2 = 1.55
VariSpot data
fCyl = +/- 500 mm
f0 = 1000 mm
= - 900 - 00 - 900
(manually rotatable mount, +/- 0.250 resolution)
Fermi-Dirac (F-D) beam profile
I(r) = I0 / {1 + exp [ (r/R0 - 1)]}
R0 = 3.25 mm
= 16.25
I0 = 0.0298 mm2
M2 (ideal F-D) = 1.50
M2 (experimental F-D) = 1.55
5. RESULTS AND DISCUSSION
Exact D() = D0 [(f02/f2) sin2() + f0
2/z2R]1/2 =
= Dm[1 + sin2()/sin2(R)]1/2
Image-mode D() D0(f0/f)sin() = DMsin()
Gaussian beam
D() vs. D() vs. sin( E = dmin/dmax vs.
Exact D() = D0 [(f02/f2) sin2() + f0
2/z2R]1/2 =
= Dm[1 + sin2()/sin2(R)]1/2
Image-mode D() D0(f0/f)sin() = DMsin()
Flat-top (Fermi-Dirac) beam
D() vs. D() vs. sin(
E = dmin/dmax vs.
Estimating the zoom range in image-mode (“angular far-field”)
D() vs. (small angles) Kurtosis vs.
Blue lines Image-mode 40
D() D0(f0/f)sin() = DMsin()
30 - 40 Zoom range in image-mode (FD FD) 13 x - 15 x
Examples of spots - Gaussian beam
Incoming gaussian beam; D0 = 4.480 mm
Gaussian beam in back-focal plane of f0 = 1 m spherical lens
Df = 0.154 mm
Examples of spots - flat-top (Fermi-Dirac) beam
Incoming Fermi-Dirac beam; D0 = 6.822 mm
Fermi-Dirac beam in back-focal plane of f0 = 1 m spherical lens
Df = 0.149 mm
Examples: VariSpot at working distance
Gaussian beam
= 500 = 100 = 40
= 500
Fermi-Dirac beam
Discussion
- Zoom (image-mode) range (DM/Dmin) scales with zR/f
- Variable spot size scales with f0
- Cheap off the shelf lenses used, no AR coating
- This arrangement already shows (13 - 15) : 1 zoom range for flat-top
profiles. Dmin 1.0 mm; DM 13.6 mm
- Estimated (20 - 50) x zoom range for flat-top profiles
- Estimated 50 m minimum spot size with flat-top profile
- Analysis smaller spots in “focus-mode”, (“Fourier-transformer-mode”,
“angular near-field”) regime (not discussed here)
Prototype
Zoom = 7 : 1
Dmin 1 mm; DM 7 mm
6. CONCLUSION
• New zoom principle demonstrated to resize a flat-top
beam at a fixed working distance
• Zoom factor (dynamic range of flat-top spot sizes):
(13 - 15) : 1
• Dmin 1.0 mm; DM 13.6 mm
• Reasonable good round spots with flat-top profiles
• Estimated results using this approach (with good
incoming flat-top beams and good optics):
Dmin 50 m
Zoom factor: (20 - 50) : 1