Holography

Holography

Zygo Corporation Copyrighted Material

Just a fancy name for Interferometry? (This copy edited for distribution)

Please do not copy material in this presentation without attribution and written consent from Zygo Corporation

Peter de Groot Digital Holography & 3-D Imaging Heidelberg, Monday, July 25, 2016 DM3I: 2:00 PM – 2:30 PM Control Number: 2519050

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©2016 Zygo Corporation and AMETEK, Inc.

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I come from ZYGO… • ZYGO makes interferometers • We measure – Distances – Form and spatial frequencies of optical parts – 3D structure of microscopic parts

Preamble…

• But we don’t do holography

Or do we?

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Once upon a time, many years ago…

What made this “holography?”

• …I did an experiment in Holography

• I wasn’t really sure why this was holography, except that I got the idea from reading the book on holographic interferometry by C.M. Vest (1979)

ultrasound

• Challenge: Quantitatively record the ultrasonic standing waves in liquid nitrogen (77.3 K), and liquid helium-II (1.60 K)

• Ever since then I have wondered… what is holography, and how does it differ from interferometry?

• Solution: Time-averaged, off-axis holographic interferometry

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The late Chuck Vest, Holoknight

Is it just in the name? de Groot, et al. Phys. Let. A 112, p.445 (1985)


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This talk… • …is about interferometry and holography—how they are the same, and how they are different • Goal: Advance interferometric metrology using ideas from holography… and perhaps the other way around as well

What is Holography?

• I also hope to challenge your thinking, just a little bit, to encourage a more “holistic” view of these two closely-related techniques


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A dictionary definition

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Nope! A typical holography setup has lots of lenses • Here is a digital holographic microscope • There are many lenses, even a microscope objective • So the “no lens” part of the definition is not helpful

“…a photographic record produced by illuminating the object with coherent light (as from a laser) and, without using lenses, exposing a film to light reflected from this object and to a direct beam of coherent light”

• Perhaps the definition of “holography” is more general

Is this the secret? T. Colomb and J. Kühn, "Digital Holographic Microscopy," in Optical Measurement of Surface Topography, R. Leach, Ed. chapt.10, (Springer, Heidelberg, 2011).


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Let’s ask an Expert!

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Here’s one way to transform phase into intensity Film

“The basic principle of holography consists in the transformation of phase changes into recordable intensity changes”

wikipedia.org/wiki/Holography

Reference wave



– Wolfgang Osten

Hologram Object wave (reflected light using the same source as the reference)

(Recording the interference intensity of the two waves with a tilt between them)

This is off-axis “Holography”

W. Osten, et al., Appl. Opt. 53, G44 (2014)


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OK well, here’s a simple tilt fringe interferometer

Wavefront phase is encoded in the tilt fringes • Historically, and even into the 1980’s, interference patterns were interpreted by hand or by computers, from the straightness of tilt fringes

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Perhaps the difference is in the Mathematics

And when we are done, what do we have?

Creating a “hologram”

Interferometry

(off-axis in x direction)

(using tilt fringes)

u  I exp  i 

 Same

Reference

u0  I 0 exp  i0 

 Yep

Add tilt fringes at an angle 

Tilt phase  2 iTx  T  directional cosine

 Same for both

Object beam

I SUM  u  u0 exp  2 iTx  

Sum Recorded hologram (interferogram?)

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I SUM   I  I 0    u*u0 exp  2 iTx    uo*u exp   2 iTx  

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• In interferometry, the object is usually simpler than a chess piece, nonetheless… • …both interferograms and holograms are complete, “holistic” representations of a wavefront frozen in time and space • Both have amplitude and phase information, often encoded in a tilt fringe, off-axis interference pattern • So holograms and interferograms look the same in classical setups…

 Looks familiar

…what about digital holography?

 No difference!


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In digital holography, we use a sensor instead of film

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Data processing using Fourier analysis The recorded intensity is

Reference wave

Digital electronic camera

I SUM   I  I 0   u*u0 exp  2 iTx    uo*u exp   2 iTx   Fourier transform



The result is

H  ,    FT I SUM     I SUM  x, y  exp  2 i  x   y    dx dy H  ,    FT I  I 0   FT u*u0      T   FT uo*u      T 

Extract the =T portion, shift to zero, and inverse transform Knowing the reference wave, reconstruct the object wave





u*u0  FT 1 FT u*u0 

u  I exp  i 

This is easier to explain with a picture…

U. Schnars and W. Jüptner, Appl. Opt. 33, 179 (1994).


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Digital processing to recover the complex amplitude Digital Fourier Transform

Original off-axis hologram recording I SUM  u  u0 exp  2 iTx  

We often refer to this as the “Takeda method” • In interferometric metrology, we sometimes analyze wavefronts using dense carrier fringes

Frequency space

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FT I SUM 

Filter

Inverse Fourier Transform

u  I exp  i 

Mitsuo Takeda

• The magnitude is used to identify valid image pixels • The phase provides the surface profile

Map of complex phase ϕ

M. Takeda, H. Ina and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry" JOSA 72 (1), 156 (1982).

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A lot has been accomplished with tilt interferometry

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So… is holography “just” interferometry?

ZEISS Direkt 100

• This might be the case for tilt-fringe interferometry

Michael Küchel

• Let’s take a closer look at this method as it is implemented in modern laser Fizeau interferometers

Tilt fringe / Deconvolution method Malgorzata Kujawinska

Klaus Freischlad

…and only rarely is it called “holography” ©2016 Zygo Corporation and AMETEK, Inc.

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Conventional phase shifting requires time… …and it is sensitive to vibration! Mechanical phase shifter

Carrier fringe instantaneous interferometry

Light source

Camera


Reference

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Object


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An alternative: “Instantaneous” interferometry

One approach is by polarization encoding

• Some environments have significant vibrations and air turbulence • All of the information required for interference fringe analysis must be gathered in less than 0.001 sec

Laser Measurement path

Camera QWP

QWP

PBS

QWP

Reference mirror

Object

Pixel-based polarizer mask After parsing pixels, duplicate images with phase shifts

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We have another view…

The tilt fringe method has advantages

• Polarization methods are, well, polarization sensitive

• Use Field Angle encoding with Carrier Fringe detection • Avoids limitations of polarization birefringence and mixing

• This means that the optical system has to be designed carefully to maintain polarization isolation

• Preserves the option for true on-axis Fizeau configuration

• Even with special care, calibration is required to mitigate residual errors, some of which cannot be avoided • All of this comes at the price of increased hardware complexity

Close up view of fringes on the camera D. M. Sykora and P. de Groot, "Instantaneous Interferometry: Another View," in Optical Fabrication and Testing, OSA OMA1 (2010).

D. M. Sykora and P. de Groot, "Instantaneous Interferometry: Another View," in Optical Fabrication and Testing, OSA OMA1 (2010).

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Fourier phase processing is “instantaneous”

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Modern systems have advanced considerably • Dense fringes for high lateral resolution • High-speed software for real-time 3D imaging

Dan Sykora

Jim Soobitsky Mike Holmes Michael Küchel Chris Evans Al Delp Jeremy Wise Thomas Dresel

• High-power (5mW) stabilized HeNe lasers for fast shuttering • in-situ compensation for wavefront errors

[ movie ]


D. M. Sykora and M. L. Holmes, Proc. SPIE 8082 (2011) D. M. Sykora and M. Kuechel US Patent 9,103,649 (Aug. 11, 2015)

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Performance is state of the art 13-Frame Phase Shifting Interferometry

PV = 0.900  RMS = 0.194 

Real-time display simplifies setup Instantaneous tilt fringe method

PV = 0.902  RMS = 0.194 

• High-quality compensation for the wavefront errors caused by part tilt • High lateral resolution reveals fine details, as in conventional PSI ©2016 Zygo Corporation and AMETEK, Inc.

[ movie ]

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Coherent noise reduction

A moving source solves the coherent noise problem

• A statistical error source in laser interferometers is spurious interference effects = coherent noise

We average multiple images with a moving source point in our CARS (coherent artifact reduction) option for the DynaFiz™ interferometer

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• This was a problem in holography from the very early days • Solution (1967): Acquire holograms under different conditions that randomize the noise, and averaging the reconstructed images

Rotating wedge plate

Left: Grey-scale surface height map by reconstruction of the object wavefront from a single DynaFiz “hologram”

Right: Improved image quality after averaging 16 images taken under different illumination conditions

Improvement with averaging > W. Martienssen and S. Spiller, Physics Letters A 24 , 126 (1967).

D. H. Close, Applied Optics 11 (2), 376 (1972).


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So…Tilt fringe interferometry: is it holography?


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Were these guys just doing interferometry?

• Tilt fringe interferometers generate off-axis digital holograms • Digital processing provides the complex phase and amplitude • Modern systems compensate for retrace errors, have high lateral resolution, and provide real-time results • Averaging techniques developed in the earliest days of holography reduce the coherent noise • Given these facts…

Holography pioneers Emmett Leith (right) and Juris Upatnieks at the Radar & Optics Lab, Willow Run Laboratories, 1964.

If so, why are they so famous? ©2016 Zygo Corporation and AMETEK, Inc.

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How does holography differ from interferometry?

The same recorded intensity pattern can be called “holographic” or “interferometric”

What makes holography so special?

The only difference, quite literally, is in how you look at it!

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Reconstructing the wavefront

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Holographic reconstruction

• In traditional holography using exposed film, the wavefront is reconstructed by illuminating it with the original reference wave

…is unique to holography

Reconstructed object wave

Hologram

• This propagating wavefront can be intercepted, focused, transformed, interpreted... from different angles and distances

Reference wave Reference wave

 Conjugate wave

This is definitely not interferometry!

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The maths tell the story…


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We can now “look” at the reconstructed wavefront

The recorded intensity is

I SUM   I  I 0   u*u0 exp  2 iTx    uo*u exp   2 iTx   If we illuminate with the tilted reference once again, we get u0 exp  iTx   H   I  I 0  u0 exp  iTx    u*u0 exp  2iTx   u0

2

u

Selecting the last term, by looking in the original direction of the object beam, we recover the complex object beam wavefront

u0

2

u


This is a unique feature of holography—the real or virtual reconstruction of propagating wavefronts by diffraction

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Digital reconstruction and propagation

Efficient calculations use plane wave decomposition

• The complex wavefront propagates to a virtual position in space using Huygens-Fresnel principle

Starting wavefront

• We use this principle to create new wavefronts anywhere along the direction of propagation

Plane-wave decomposition “Propagation” of plane waves to a new z position

Starting wavefront

u  x, y   I  x, y  exp i  x, y 

U  ,      u  x, y  exp  2 i k  x   y   dx dy ...where k  1  and  ,   directional cosines

U NEW  ,  , z   U  ,   exp  2 i k z 1   2   2   

Resulting wavefront

(measured using interferometry)

(calculated by adding up all the individual contributions)

Reconstruction of the new wavefront

uNEW  x, y , z     U NEW  ,  , z  exp  2 ik  x   y   k 2d d 

See J. W. Goodman, "Introduction to Fourier Optics"

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Diffractive optics for testing aspheres are holographic


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Holographic optics at ZYGO

• We tend to call them “diffractive optics” today, but in the early days, they were “synthetic holograms”

Custom “CGH” (computer generated hologram) D. Bajuk, B. Kestner, "40 Years of Freeform Optics,“ Zygo Extreme Precision Optics (2012).

Prof. J. Schwider

Hubble Space Telescope correction optics qualified using CGH null correctors

D. Malacara, K. Creath, J. Schmit and J. C. Wyant, in "Optical shop testing,“ (2007). C. Pruss, E. Garbusi and W. Osten, “Testing Aspheres” Opt. and Phot. (2008)

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Some “interferometers” use classical holography LED light source Holographically-generated linear gratings Camera

Conclusions

Reconstructed object and conjugate beams

The object goes here

P. de Groot, "Diffractive grazing-incidence interferometer,“ Applied Optics (2000)


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Many interferometers almost use holography

So.. is holography just a fancy name for interferometry? • No! • The creation of the original hologram is indeed interferometry, however… • …interferometric metrology usually does not involve the regeneration or digital synthesis of a propagating wavefront

• They perform the first step of holistically measuring and recording the wavefront complex amplitude—both phase and magnitude • The recording geometry can be identical to the traditional off-axis holographic exposure


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Why is this useful to know? • Ideas carried over from holography have enriched interferometric metrology

Thanks to Les Deck Xavier Colonna de Lega Jan Liesener Michael Turzhitsky

• The same effect has occurred in the other direction—holograms are sometimes acquired digitally using phase shifting methods • Conclusion: There is practical value in comparing the two methods, how they differ, and how they are converging towards a common set of techniques to solve challenging tasks


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