Page 1 @Dept. of Physics, Gauhati University
Dynamic beam shaping with programmable diffractive optics
Bosanta R. BoruahDept. of Physics, GU
Page 2 @Dept. of Physics, Gauhati University
Outline of the talk
• Introduction– Holography– Programmable diffractive optics
• Laser scanning confocal microscopy (LSCM)– Aberration correction in LSCM
• Programmable reference phase stepping interferometry
• Conclusion
Page 3 @Dept. of Physics, Gauhati University
The principle of holography
Reference plane wave
Object beam
Resulting interferencepattern
Crest
Trough
Page 4 @Dept. of Physics, Gauhati University
The principle of holography
f f
+1 0 -1
transmittance=1
transmittance=0
hologram lens diffraction pattern(Fourier plane of the hologram)
Incident coherentbeam (reference)
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diffracted beams
Reconstructed object beamConjugate beam
Page 5 @Dept. of Physics, Gauhati University
Phase only hologram
f f
-1 0 1
phase delay=π
phase delay=0
lens diffraction pattern
-1 +1+1 -1
Phase hologram
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Binary phase only hologram
f f
-1 0 1
phase delay=π
phase delay=0
lens diffraction pattern
-1 +1
Binary phasehologram
+7 +5 +3 +1
Page 7 @Dept. of Physics, Gauhati University
glass plates
transparent electrodes
alignment layers
V
liquidcrystal4×4 pixels
(can go upto 2Kx1K)
Liquid crystal spatial light modulator (LCSLM)
SLM panel~10 µm
Page 8 @Dept. of Physics, Gauhati University
alignment layer
glass platemirror
alignment layer
glass platemirror
Emax
(a) (b)
NLC molecules
Nematic LC pixel
• Analog phase modulation• Response time of the molecules :~ms• Frame rate :60Hz• Light efficiency :50%
Page 9 @Dept. of Physics, Gauhati University
E+ E-
d
p
s /p
PBS
FLC cell
z
Director axis :(view along z)
on off
Ferroelectric LC pixel
• Binary amplitude or phase (0 or π) modulation• Response time of the molecules :~10µs• Frame rate :1440 Hz• Light efficiency (amplitude modulation) : 70%
Page 10 @Dept. of Physics, Gauhati University
Binary Hologram Design for phase and amplitude modulation
Complex amplitude over the pupil plane (x,y) = a(x,y) eiφ(x,y)=u(x,y)+iv(x,y)
a(x,y) = normalised amplitude=
φ(x,y) = desired phase+overall tilt=
S(mx, my)=Phase delay at (mx, my)
Pupil planeF (ferroelectric) LCSLM plane
[u(x,y) ,v(x,y)]
Binary phase mapping
22 vu +
vu1tan −
(mx, my)(m=magnification factor)
Page 11 @Dept. of Physics, Gauhati University
Binary phase mapping algorithm
u
v
0π
Complex amplitude desired = [u(x,y), v(x,y)]
Binary phase mapφ(x, y) → S(mx,my)
Off-axis hologram on FLCSLM
Desired amplitude profileIn the pupil plane
|amplitude|=1
|amplitude|=0
Page 12 @Dept. of Physics, Gauhati University
Binary phase mapping algorithm
Complex amplitude over the pupil plane (x,y) = eiφ(x,y) such that a(x,y)=1
S(mx, my) =0 if cos(φ(x,y))>0=π if cos(φ(x,y))<0
Off-axis hologram on FLCSLM
Desired amplitude profileIn the pupil plane
Phase delayQuickTime™ and a
TIFF (Uncompressed) decompressorare needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Page 13 @Dept. of Physics, Gauhati University
Generation of arbitrary complex amplitude profile
Laser beam
FLCSLM
Hologram
Desired complexamplitude in thepupil plane
Iris diaphragm
Page 14 @Dept. of Physics, Gauhati University
Wide field microscope
• Collimated beam of wavelength λ is focused by L1 to a diffraction limited volume
• The illumination volume depends on λ, focal length and diameter of the illumination lens
• A point object is imaged into a diffraction limited volume in the image space• Resulting image has poor axial resolution
object
image
Ref
lect
ed li
ght
IlluminationLens (L1)
Detectionlens
Beam splitter
Diffraction limitedillumination volume
Pointsource
Page 15 @Dept. of Physics, Gauhati University
Optical sectioning in a confocal microscope
detector
detection lens
pin hole
Laserbeam
detectorpin hole
Laserbeam
Illumination lens
Sampleplane
Sampleplane
• Confocal arrangement of focal point and pinhole blocks light from out of focus planes or points away from the optic axis
• The detector receives light mostly from the focal point– Image, free of out of focus blur, of a point object located at the focal point
Focalpoint
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Optical sectioning in a confocal microscope
detector
BS
scan
Wide field image Confocal image
(Source :www.olympusfluoview.com)
PC
• Either the sample holding stage or the illumination spot is scanned– Scanning is controlled by a PC
• For each object point at the illumination spot, the detector signal is stored in the PC• Results in an optically sectioned image (image corresponds to a sharply defined object
plane, devoid of out of focus blur) of the sample• Much better axial and marginally better lateral resolutions than a conventional (wide
field) microscope
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ZernikeModes
PSFs
Entrance pupil
Unaberrated wavefront
Aberrated wavefront
PSF for an unaberrated Beam, Airy discLensW(x, y)
Point spread function(PSF)
Effects of aberrations
• Presence of aberrations in the illumination beam effects the performanceof the confocal microscope
• Need for aberration compensation
Page 18 @Dept. of Physics, Gauhati University
Detectorpin hole
Incident aberrated beam
50/50 beam splitter Positive bias plate
Negative bias plate
mirror
I2(0) I1(0)
Sensor signal=I2(0)-I1(0)
I1(0)
I2(0)
Modal wavefront sensor
• Positive and the negative bias plates adds and subtracts a certain of a zernike mode aberration
• LCSLM assembly can be used to detect and correct aberrations in terms of various zernike modes
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Modal wavefront sensor (results)
biased orders(Z4)
biased orders(Z6)
PSF
before correction after correction
Peak intensity improves by a factor of three
Page 20 @Dept. of Physics, Gauhati University
Aberration sensitivity and correction using a helical beam
Low NA aberrated PSFs to 0.8 Strehl ratio in normal beam (normally considered well corrected)
Normal beam
Helical beam
Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z14 Z15
• Helical type beams are highly sensitive to azimuthally dependent aberrations!
Helical phase profileacross the pupil
0
2π
d1
d2d3d4
d5
d6
d7
d8d9 d10
d11d12
Sensorcircle
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Low NA aberration correction demonstration
(a)
(b)
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0 1 2 3 4 5 6 7 8
Iteration
(a)(b)
Drop due toslide reflectivity
(a) With aberrated test slide (b) With initial offset aberration
(1.4 radian RMS)
PSF (helical beam) PSF (normal beam)
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Laser
L1 L2 BS
CCD
L3
L4
Reference mirrorwith PZT
Test Mirror
Reference motion
Phase stepping interferometry
• Reference mirror stepped n times with a step size λ/(2n)• CCD records n interference patterns, where n>2• Intensity at a CCD pixel as a function of step index is a sine wave
– Surface profile of the test mirror manifests as phase delay• Not effected by the inhomogenity in the beam intensity profile• No fringe centering required• Does not depend on the number of fringes
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Laser
L1 L2 λ/2
CCD
L3
L4
Test Mirror
control unit
BS
λ/4
polariser
FLCSLM
iris diaphragm
Programmable reference PSI
• Accurate and repeatable phase stepping• Reference wavefront can be programmed to match the test
surface• Accuracy in phase measurements are effected by aliasing
Page 24 @Dept. of Physics, Gauhati University
Aliasing
Profile to be sampled
After sampling
phase
φ (x)
S(x)
N*2π
N square waves
In disguise as low frequencysquare wave, if no of pixels for N squarewaves <2N
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Random binarisation to remove aliased orders
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
v
u
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
-1-5
+3
+1+5
-3
-1
+1
S(x, y)=[cos(φ(x, y)<Rand(x,y)] π
Fourier plane of a randomlyBinarised hologram
Fourier plane of a binarisedhologram
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Phase profile using 24 bit random binarization
Normal binarization 24 bit random binarization
Blue → red → yellow → green → bluePhase: 0 → 2π
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Conclusion
• Generation of arbitrary wavefront using an LCSLM– accurate, fast and with excellent repeatability
• LCSLM can be used both for detection and correction of optical aberrations
• Can used in a phase stepping interferometer to generate the reference beam
• Poor light efficiency– May effect its applicability to other areas
Page 28 @Dept. of Physics, Gauhati University
Thank You