digital holography

In the off-axis configuration, a small angle between the reference and the object beams is used to prevent overlapping of the cross-beating contributions between the object and reference optical fields with the self-beating contributions of these fields. These discoveries were made by Emmett Leith and Juris Upatnieks for analog holography,{{cite journal | last1 = Leith | first1 = E. N. | last2 = Upatnieks | first2 = J. | year = 1962 | title = Reconstructed wavefronts and communication theory | journal = JOSA | volume = 52 | issue = 10| pages = 1123–1128 | doi=10.1364/josa.52.001123| bibcode = 1962JOSA...52.1123L }} and subsequently adapted to digital holography. In this configuration, only a single recorded digital interferogram is required for image reconstruction. Yet, this configuration can also be used in conjunction with temporal modulation methods, such as phase-shifting and frequency-shifting for high sensitivity measurements in low light.Gross, Michel, and Michael Atlan. "Digital holography with ultimate sensitivity." Optics letters 32, no. 8 (2007): 909-911.

The phase-shifting (or phase-stepped) digital holography process entails capturing multiple interferograms that each indicate the optical phase relationships between light returned from all points on the illuminated object and a controlled reference beam of light. The optical phase of the reference beam is shifted from one sampled interferogram to the next. From a linear combination of these interferograms, complex-valued holograms are formed. These holograms contain amplitude and phase information of the optical radiation diffracted by the object, in the sensor plane.{{cite journal | last1 = Yamaguchi | first1 = I. | last2 = Zhang | first2 = T. | title = Phase-shifting digital holography | journal = Opt. Lett. | volume = 22 | issue = 16| pages = 1268–1270 | doi=10.1364/ol.22.001268|bibcode = 1997OptL...22.1268Y | year = 1997 | pmid = 18185816 }}

Through the use of electro-optic modulators (Pockel cells) or acousto-optic modulators (Bragg cells), the reference laser beam can be frequency-shifted by a tunable quantity. This enables optical heterodyne detection, a frequency-conversion process aimed at shifting a given radiofrequency optical signal component in the sensor's temporal bandwidth. Frequency-shifted holograms can be used for narrowband laser Doppler imaging.{{cite journal | last1 = Atlan | first1 = M. | last2 = Gross | first2 = M. | last3 = Forget | first3 = B. | last4 = Vitalis | first4 = T. | last5 = Rancillac | first5 = A. | last6 = Dunn | first6 = A. | title = Frequency-domain wide-field laser Doppler in vivo imaging | url = https://hal.archives-ouvertes.fr/hal-00258697/document| journal = Opt. Lett. | volume = 31 | issue = 18| pages = 2762–2764 | doi=10.1364/ol.31.002762|bibcode = 2006OptL...31.2762A | year = 2006 | pmid = 16936884 }}

Addressing simultaneously distinct domains of the temporal and spatial bandwidth of holograms was performed with success for angular,{{cite journal | last1 = Paturzo | first1 = M. | last2 = Memmolo | first2 = P. | last3 = Tulino | first3 = A.|author3-link=Antonia Tulino | last4 = Finizio | first4 = A. | last5 = Ferraro | first5 = P. | year = 2009 | title = Investigation of angular multiplexing and de- multiplexing of digital holograms recorded in microscope configuration | journal = Opt. Express | volume = 17 | issue = 11| pages = 8709–8718 | doi=10.1364/oe.17.008709| pmid = 19466119 |bibcode = 2009OExpr..17.8709P | doi-access = free }} wavelength,{{cite journal

| author=J. Kühn

|author2=T. Colomb |author3=F. Montfort |author4=F. Charrière |author5=Y. Emery |author6=E. Cuche |author7=P. Marquet |author8=C. Depeursinge

| title=Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition

| journal=Optics Express

| volume=15

|issue=12

| pages=7231–724

| year=2007

| doi=10.1364/OE.15.007231

|bibcode = 2007OExpr..15.7231K | pmid=19547044|doi-access=free}}Tomohiro Kiire, Daisuke Barada, Jun ichiro Sugisaka, Yoshio Hayasaki, and Toyohiko Yatagai. "Color digital holography using a single monochromatic imaging sensor. Opt. Lett. 37(15):3153–3155, Aug 2012. space-division,{{cite journal | last1 = Tahara | first1 = Tatsuki | last2 = Maeda | first2 = Akifumi | last3 = Awatsuji | first3 = Yasuhiro | last4 = Kakue | first4 = Takashi | last5 = Xia | first5 = Peng | last6 = Nishio | first6 = Kenzo | last7 = Ura | first7 = Shogo | last8 = Kubota | first8 = Toshihiro | last9 = Matoba | first9 = Osamu | title = Single-shot dual- illumination phase unwrapping using a single wavelength | journal = Opt. Lett. | volume = 37 | issue = 19| pages = 4002–4004 | doi=10.1364/ol.37.004002|bibcode = 2012OptL...37.4002T | year = 2012 | pmid = 23027259 }} polarization,{{cite journal

| author1=T. Colomb

| author2=F. Dürr|author3=E. Cuche|author4=P. Marquet|author5=H. Limberger|author6=R.-P. Salathé|author7=C. Depeursinge

| title=Polarization microscopy by use of digital holography: application to optical fiber birefringence measurements

| journal=Applied Optics

| volume=44

|issue=21

| pages=4461–4469

| year=2005

| doi=10.1364/AO.44.004461

| pmid=16047894|bibcode = 2005ApOpt..44.4461C }} and sideband{{cite journal |author=N. Verrier |author2=M. Atlan |title=Absolute measurement of small-amplitude vibrations by time-averaged heterodyne holography with a dual local oscillator |journal=Optics Letters |volume=38 |issue=5 |pages=739–41 |year=2013 |arxiv=1211.5328|doi=10.1364/OL.38.000739 |pmid=23455283 |bibcode=2013OptL...38..739V }}{{cite journal |author=Bruno, F. |author2=Laudereau, J. B. |author3=Lesaffre, M. |author4=Verrier | author5=Atlan, M.|title=Phase-sensitive narrowband heterodyne holography |journal=Applied Optics |volume=53 |issue=7 |pages=1252–1257 |year=2014 |arxiv=1301.7532|doi=10.1364/AO.53.001252|pmid=24663351 |bibcode=2014ApOpt..53.1252B }} multiplexing schemes. Digital holograms can be numerically multiplexed and demultiplexed for efficient storage and transmission. Amplitude and phase can be correctly recovered.{{cite journal |title=Numerical multiplexing and demultiplexing of digital holographic information for remote reconstruction in amplitude and phase |author=M. Paturzo |author2=P. Memmolo |author3=L. Miccio |author4=A. Finizio |author5=P. Ferraro |author6=A. Tulino|author6-link=Antonia Tulino |author7=B. Javidi |journal=Optics Letters |volume=33 |pages=2629–2631 |year=2008 |doi=10.1364/OL.33.002629 |pmid=19015690 |issue=22|bibcode = 2008OptL...33.2629P }}

Super-resolution is possible by means of a dynamic phase diffraction grating for increasing synthetically the aperture of the CCD array.{{cite journal | last1 = Paturzo | first1 = M. | last2 = Merola | first2 = F. | last3 = Grilli | first3 = S. | last4 = Nicola | first4 = S. De | last5 = Finizio | first5 = A. | last6 = Ferraro | first6 = P. | year = 2008 | title = Super-resolution in digital holography by a two-dimensional dynamic phase grating | journal = Optics Express | volume = 16 | issue = 21| pages = 17107–17118 | doi = 10.1364/OE.16.017107 | pmid=18852822|bibcode = 2008OExpr..1617107P | doi-access = free }} Super-localization of particles can be achieved by adopting an optics/data-processing co-design scheme.{{cite journal | last1 = Verrier | first1 = N. | last2 = Fournier | first2 = C. | last3 = Cazier | first3 = A. | last4 = Fournel | first4 = T. | year = 2016 | title = Co-design of an in-line holographic microscope with enhanced axial resolution: selective filtering digital holography | journal = J. Opt. Soc. Am. A | volume = 33 | issue = 1| pages = 107–116 | doi =10.1364/JOSAA.33.000107| pmid = 26831591 | arxiv = 1601.02940 | bibcode = 2016JOSAA..33..107V }}

Optical sectioning, also known as sectional image reconstruction, is the process of recovering a planar image at a particular axial depth from a three-dimensional digital hologram. Various mathematical techniques have been used to solve this problem, with inverse imaging among the most versatile.{{cite journal

| author=P.W.M. Tsang

|author2=K. Cheung |author3=T. Kim |author4=Y. Kim |author5=T. Poon

| title=Fast reconstruction of sectional images in digital holography

| journal=Optics Letters

| volume=36

| issue=14

| pages=2650–2652

| year=2011

| doi=10.1364/OL.36.002650

| pmid=21765497

| bibcode=2011OptL...36.2650T

}}{{cite journal

| author1=E. Lam

| author2=X. Zhang|author3=H. Vo|author4=T.-C. Poon|author5=G. Indebetouw

| title=Three-dimensional microscopy and sectional image reconstruction using optical scanning holography

| journal=Applied Optics

| volume=48

|issue=34

| pages=H113–H119

| year=2009

| doi=10.1364/AO.48.00H113

| pmid=19956281

|bibcode = 2009ApOpt..48..113L | hdl=10919/46969| hdl-access=free

}}{{cite journal

| author1=X. Zhang

| author2=E. Lam|author3=T.-C. Poon

| title=Reconstruction of sectional images in holography using inverse imaging

| journal=Optics Express

| volume=16

|issue=22

| pages=17215–17226

| year=2008

| doi=10.1364/OE.16.017215

| pmid=18958002|bibcode = 2008OExpr..1617215Z | hdl=10919/46959

| hdl-access=free

}}

By using the 3D imaging capability of Digital Holography in amplitude and phase it is possible to extend the depth of focus in microscopy.{{cite journal | last1 = Ferraro | first1 = P. | last2 = Grilli | first2 = S. | last3 = Alfieri | first3 = D. | last4 = Nicola | first4 = S. De | last5 = Finizio | first5 = A. | last6 = Pierattini | first6 = G. | last7 = Javidi | first7 = B. | last8 = Coppola | first8 = G. | last9 = Striano | first9 = V. | year = 2005 | title = Extended focused image in microscopy by digital holography | journal = Optics Express | volume = 13 | issue = 18| pages = 6738–6749 | doi = 10.1364/OPEX.13.006738 |bibcode = 2005OExpr..13.6738F | pmid=19498690| doi-access = free }}

The digital analysis of a set of holograms recorded from different directions or with different direction of the reference wave allows the numerical emulation of an objective with large numerical aperture, leading to corresponding enhancement of the resolution.{{cite journal

| author=Y.Kuznetsova

|author2=A.Neumann, S.R.Brueck

| title=Imaging interferometric microscopy–approaching the linear systems limits of optical resolution

| journal=Optics Express

| volume=15

|issue=11

| pages=6651–6663

| year=2007

| doi=10.1364/OE.15.006651

| bibcode=2007OExpr..15.6651K

| pmid=19546975

| doi-access=free

}}{{cite journal

| author=C.J.Schwarz

|author2=Y.Kuznetsova and S.R.J.Brueck

|s2cid=31379

| title=Imaging interferometric microscopy

| journal=Optics Letters

| volume=28

| pages=1424–1426

| year=2003

| doi=10.1364/OL.28.001424

| pmid=12943079

| issue=16

|bibcode = 2003OptL...28.1424S }}{{cite journal |title=Super-resolution in digital holography by a two-dimensional dynamic phase grating |author=M. Paturzo |author2=F. Merola |author3=S. Grilli |author4=S. De Nicola |author5=A. Finizio |author6=P. Ferraro |journal=Optics Express |volume=16 |pages=17107–17118 |year=2008 |doi=10.1364/OE.16.017107 |pmid=18852822 |issue=21|bibcode = 2008OExpr..1617107P |doi-access=free }} This technique is called interferometric microscopy.

• Computer generated holography
• Digital holographic microscopy
• Holographic interferometry
• Holography

{{reflist}}

• {{cite journal | last1 = Grilli | first1 = S. | last2 = Ferraro | first2 = P. | last3 = Nicola | first3 = S. De | last4 = Finizio | first4 = A. | last5 = Pierattini | first5 = G. | last6 = Meucci | first6 = R. | year = 2001 | title = Whole optical wavefields reconstruction by digital holography | journal = Optics Express | volume = 9 | issue = 6| pages = 294–302 |bibcode = 2001OExpr...9..294G |doi = 10.1364/OE.9.000294 | pmid = 19421300 | doi-access = free }}

Category:Holography