Programmable CGH on photochromic material using DMD generated masks

2018 Publication Year

2020-11-16T12:28:14Z Acceptance in OA@INAF

Programmable CGH on photochromic material using DMD generated masks Title

Alata, Romain; Zamkotsian, Frédéric; Lanzoni, Patrick; PARIANI, Giorgio; Bianco, A.; et al. Authors 10.1117/12.2292075 DOI http://hdl.handle.net/20.500.12386/28355 Handle PROCEEDINGS OF SPIE Series 10546 Number

PROCEEDINGS OF SPIE

SPIEDigitalLibrary.org/conference-proceedings-of-spie

Programmable CGH on

photochromic material using DMD

generated masks

Romain Alata, Frédéric Zamkotsian, Patrick Lanzoni,

Giorgio Pariani, Andrea Bianco, et al.

Romain Alata, Frédéric Zamkotsian, Patrick Lanzoni, Giorgio Pariani,

Andrea Bianco, Chiara Bertarelli, "Programmable CGH on photochromic

material using DMD generated masks," Proc. SPIE 10546, Emerging Digital

Programmable CGH on photochromic material

using DMD generated masks

Romain Alata

, Frederic Zamkotsian

, Patrick Lanzoni

,

Giorgio Pariani

, Andrea Bianco

, Chiara Bertarelli

1 _{Aix Marseille Université, CNRS, LAM (Laboratoire d'Astrophysique de Marseille), 13388, Marseille, France} 2 _{INAF – Osservatorio Astronomico di Brera, Via Bianchi 46, 23807 Merate, Italy}

3 _{Politecnico di Milano, Dipartimento di Chimica, Materiali e Ingegneria, p.zza L. Da Vinci 32, 20133, Milano, Italy}

e-mail: frederic.zamkotsian@lam.fr

ABSTRACT

Computer Generated Holograms (CGHs) are used for wavefront shaping and complex optics testing, including aspherical and free-form optics. Today, CGHs are recorded directly with a laser or intermediate masks, allowing only the realization of binary CGHs; they are efficient but can reconstruct only pixilated images. We propose a Digital Micro-mirror Device (DMD) as a reconfigurable mask, to record rewritable binary and grayscale CGHs on a photochromic plate. The DMD is composed of 2048x1080 individually controllable micro-mirrors, with a pitch of 13.68 µm. This is a real-time reconfigurable mask, perfect for recording CGHs. The photochromic plate is opaque at rest and becomes transparent when it is illuminated with visible light of suitable wavelength. We have successfully recorded the very first amplitude grayscale CGH, in equally spaced levels, so called stepped CGH. We recorded up to 1000x1000 pixels CGHs with a contrast greater than 50, using Fresnel as well as Fourier coding scheme. Fresnel’s CGH are obtained by calculating the inverse Fresnel transform of the original image at a given focus, ranging from 50cm to 2m. The reconstruction of the recorded images with a 632.8nm He-Ne laser beam leads to images with a high fidelity in shape, intensity, size and location. These results reveal the high potential of this method for generating programmable/rewritable grayscale CGHs, which combine DMDs and photochromic substrates.

Key words: Computer Generated Hologram, CGH, programmable CGH, MOEMS, photochromic material,

optical testing, wavefront shaping, DMD.

1. INTRODUCTION

Computer Generated Holograms (CGHs) are useful for wavefront shaping and complex optics testing, including aspherical and free-form optics [1]. CGHs are classified in two groups: 1- phase holograms, which are obtained by recording a phase variation in a material having a modulated refractive index or thickness; 2- amplitude holograms, where an intensity pattern is recorded in a material whose transparency can be locally controlled. Phase and amplitude holograms provide the same performances in terms of image reconstruction quality, but different diffraction efficiency. For instance, binary phase holograms, show 40% diffraction efficiency in the first order, whereas efficiency is limited to 10% for binary amplitude holograms [2]. Therefore, amplitude holograms are usually applied in interferometry, which is not intensity limited.

Grayscale amplitude and grayscale phase holograms are known to give a higher reconstruction quality than binary holograms [2], but they require a more complex production process. Specifically, the production of phase grayscale CGHs is complex since a series of masks has to be consecutively aligned very precisely, and a developing step is required after each exposure step to obtain the final hologram.

To our best knowledge, only grayscale phase CGHs have been obtained so far by micro-lithography [3], the uniformity of the material thickness being the main limiting parameter for these components [4]. Concerning amplitude CGHs, they are nowadays produced in chrome on glass by means of lithographic techniques, either mask or maskless (by direct writing) lithography. Due to the binary nature of the chrome developing process, these techniques allow for easily writing binary CGHs, but they cannot provide grayscale CGHs.

In this paper, we demonstrate an original recording technique, which makes use of a programmable mask and a non-threshold photosensitive material, to produce ready to use grayscale CGHs in a one exposure process without requiring any developing step. Indeed, a set-up based on a Digital Micro-mirror Device (DMD), which has been originally developed to generate programmable slit masks in multi-object spectrographs [5], is considered. DMDs are programmable devices, composed of millions of micro-mirrors reconfigurable in real time. Actually, DMDs have been extensively used to generate dynamic binary or grayscale holograms [6], by exploiting the fast switching of the mirrors at frequencies higher than the human vision frame rate. The grayscale originates as a dynamic effect and not as a steady state effect. However, the discrete structure of the device induces a high scattering and background noise from the mirrors edges when illuminated with laser light [7], making such holograms useless for interferometry and metrology. Nevertheless, DMDs perfectly reproduce binary masks to be projected with incoherent light on photosensitive plates, thus producing amplitude CGHs. In this work, such plate consists in a photochromic film that can be reversibly converted from an opaque and colored form to a transparent form upon exposure with light of suitable wavelengths [8]. Actually, reversible holograms have been already obtained with photochromic materials [9, 10] and real-time photochromic holograms were shown, by exploiting the fast transition of imidazole dimers [11, 12]. Moreover, photochromic binary CGHs for optical testing have been recently demonstrated [13]. In photochromic materials, a ready to use hologram is generated just after the light exposure, and the reversibility of the photoconversion makes devices rewritable. Even more interesting, the transparency of a photochromic layer can be tuned by the dose of light absorbed, which opens to the development of grayscale patterns [14]. In fact, the DMD set-up allows for easily recording grayscale CGHs with equidistant transparency levels, named as stepped CGHs, in a single exposure process. The lower diffraction efficiency of grayscale amplitude holograms with respect to binary amplitude holograms (6% vs. 10% [2]) is here compensated by a better image reconstruction quality, an easy exposure process and no developing steps, which are the limiting factors in the production of grayscale phase holograms.

In this paper, we report on the first stepped CGHs and results are compared to binary CGHs. We read the recorded information using a low power 632.8 nm laser, and the whole hologram is erased with a UV flash, for a reusable substrate.

2. RECORDING AND RECONSTRUCTION OF A CGH

We developed 2 set-ups, respectively dedicated to the recording of the calculated CGH and the reconstruction of the original encoded images.

2.1 Recording set-up

Figure 1 shows our first set-up, dedicated to the CGH recording on the photosensitive plate. The DMD, controlled by the formatter board [15] is illuminated by a collimated beam from a white source, and redirects the light toward the plate. The beam is illuminating the entire DMD and the light power is homogeneous on the plate. The pattern reproduced by the DMD has to be projected onto the plate as precisely as possible, so the plate is illuminated through an Offner relay with a magnification of 1:1. This relay provides a nearly aberration free beam and has the advantage of being compact. The unit magnification means that the maximum size of CGH is directly limited by the size of the DMD; the micro-mirrors of the DMD therefore correspond to the “pixels” of the CGH. Finally, a post-CGH imaging system located right after the CGH plate consists of two lenses, a filter around 600 nm and a CCD camera. This system in an afocal assembly allows imaging of the CGH during writing, in situ and in real time. Magnification is tuned by changing properly the pair of lenses, from a value of 1 up to 4.

DMD, CGH and camera planes are then conjugated. Note that DMD plane is a tilted focal plane due to the nature of micro-mirror array: each micro-mirrors tilts out of the array plane by 12°, leading to a global 24° tilted focal plane. This effect is reproduced as well at the post-CGH imaging camera level (the camera plane is tilted by 24°).

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r 500 cycles b have also been

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Fig. 2: DMD

et-up dedicated n imaging optic D plane to the C

rom Texas Ins 48 x 1080 mi on and an OF hnical assessm mission). Spec e DMD remai vacuum) has between room n done; no deg the ability of

chip from Tex

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uld act as rec .68µm pitch, sition (Fig. 2) this DMD com ng electronics ational at -40° sfully complet and cold tem bserved from meet environ (2048 x 1080 m d on an illumina nification Offne maging system. onfigurable m where each m ). This compo mponent (204 s and a cold te °C and in vacu ted. Total Ion

perature, on a the optical me nmental spac micromirrors). ation unit er relay mask generato mirror can be onent has bee 48 x 1080 mirr emperature te uum. A 1038 nizing Dose (T a non-operatin measurements. ce requiremen

or. The larges independently en extensively rors) for space est set-up have hours life tes TID) radiation ng device) and These results nts [15]. st y y e e st n d s

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ake the system nto the CGH p eters are <20µ Fig. nt wavelengths a ace: IMA 00, 7.50 mm velength-> eld : 00, 7.50 mm 00, 0.00 mm 00, -7.50 mm 00, -7.50 mm 00, 0.00 mm 00, 0.00 mm 00, 7.50 mm 0, -7.50 mm TNG offner spectr 1/2011 Units are µ width : 70

has been set u ors belong to ed instead of can lead to s d a radius of Fig. 3: Optical m simple and e plane is high e µm over the w 4: Imagery spo and field of view

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2.2 R

The second s laser. The cam section, the F focus. It is th Fourier holog collimation ca Fig. 5: Pictu The photosen large content uncolored for transparent fo Figure Reconstructio set-up, shown mera, placed Fresnel hologr hus not necess grams. This i

an displace th

ure of the set-up

nsitive materia of photochro rms, also for orm upon expo

e 6: Transmissi showing

on set-up

n in Fig. 5, is at the distanc rams are direc sary to add a s why the sou he focal plane

p dedicated to im located

al is a diaryle omic units (i.e thin films. T osure with lig

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mage reconstru at the hologram

3. PHOTO ethene-based p e. 50% wt. in This layer can ht of suitable nsity) of the ph he transparent s CGH reconst e plate, is illu d from the pr

the plate and be rigorously ical axis and c

uction, including m projection dis OCHROMIC polyurethane this work) th n be reversibl wavelengths, hotochromic ma states, accordin truction. The uminated thro opagation equ d the camera t collimated, b change the siz

g a 632.8 nm H stance (2m in th

C PLATES [17]. Such ki hat turns into ly converted around 600nm aterial used in th ng to the illumin source is a c ugh the CGH uations of ligh to reconstruct because a var ze of the encod

He-Ne laser, the his case). nd of photoch a high contra from an opaq m (Fig. 6) he UV-Visible r nation amount o collimated 632 H. As describe ht, and they a t the image, u riation in the ded image. CGH plane an hromic substr ast between th que and colo

range of the sp of the plate

2.8 nm He-Ne ed in the nex are for a given unlike with the quality of the d the camera rate contains a he colored and red form to a ectrum e xt n e e a d a

Moreover, the and the film photochromic function of th CGHs could b 4.1 F Fourier holog reproduced. T calculated, th the used algo defining the i 2048x1080 m maximum att Since these reconstruction could be calcu 4.2 F Fresnel holog Sommerfeld i The resulting anywhere on by the transm by its comple the skew facto The distance dimensions, t Where the ke The equation encoded imag desired focal The convolut

The first obje Fig 7(a), with cover the 1 in resolution of smaller than insufficient b e optical qual is set uniform c film has be he film feature be calculated Fourier holog grams are ob These algorith he complex inf rithm. The nu image. This le micro mirrors tainable resolu holograms ar n set-up, for a ulated very fa Fresnel holog

grams are dire integral diffra

g complex wav the screen loc mittance t(x, y) ex amplitude A or and is equa z between th the equation (1 ernel convoluti n (2) simulate ge, the develo

length z. tion function i ect to be recor h a physical s nch square su 720x720 pixe the CGH, is ecause the frin

lity in terms o mly to the op een previously es and illumin as Fourier hol grams btained using hms [18, 19, formation con umber of pixe eads to limita and the dime ution of the im

re based on applying the o ast but they wi

grams ectly calculate action given in ve Az is estim cated at a dist ) of the hologr A0 and its wav al to zero in ou he hologram a 1) can be appr ion hz, called es the diffract opment of thi s defined by t

ded on the pla ize of 2x2mm upport plate, a

els. The physi s surrounded nges on the co of transparency paque state by y determined ation conditio 4. CGH lograms and F g algorithms 20] are oper ntained in eac ls of a Fourier ting the resolu nsions W and mage to be enc the Fourier optical Fourie ill not be discu

ed with the li n equation 1 [2 mated by calcu tance z. Each ram. These se velength λ (or ur configuratio nd the screen roximated by Fresnel functi tion of the re is reconstruct the equation (4 5. B ate is the binar m2 _{and calcula} a maximum C ical dimension by the Fresn orner will be t y and scatterin y a UV expo d by a kinetic ons [14]. Hs CALCUL Fresnel hologr encoding the rating in a c ch pixel is enc r hologram is ution and size d H being 4 p coded is 250x2 transform, it er transform to ussed in this p ight propagati 21]. ulating the su pixel is consi econdary wave r the wave nu on. n being much the following ion, is: ference wave tion being obt

4): BINARY CG ry CGH of the ated at a focus GH dimensio ns of the “Z” nel lens patter

too close.

ng is very goo osure. The con c model that LATION rams. In this p e inverse Fou ommon way. coded in a cell therefore nec e of images to pixels or large 250 pixels, an is necessary o the CGH, an paper. ion equations um of the con idered as a se es are generate umber k = 2π/ greater than t g 2D convoluti e on the holog tained by esti GH e letter “Z”, fo s of 2m. As th on of 1cmx1cm ” are fixed as rn. With a lo

od. The photo nversion unde provides the paper we will f urier transform Once the in l of WxH pixe cessarily large o be encoded. er, with the m nd its actual si y to add a le nd display the , and can be ntributions of condary spher ed when the in /λ), reaches th the dimension ion product :

gram and thu imating the c

ormed on a 10 he photosensi m has been fix

1/5 of the CG onger CGH th ochromic plate er light illum degree of tra focus on Fres m of the wa nverse Fourier els, W and H er than the num

. The DMD is most compact

ize is limited t ens after the e image. Four modeled by t each pixel of erical wave so ncident wave, he hologram. T ns of the dete us reconstruct convolution ke 0x10 pixel gri itive material ixed, which le GH dimension he resolution e is 3µm thick mination of the ansparency as nel CGHs. avefront to be r transform is depending on mber of pixels s composed o algorithm, the to 3,4x3.4mm CGH in the rier holograms the Rayleigh f the hologram urce weighted , characterized The angle  is ctor and CGH s the digitally ernel hz at the d as shown on does not fully eads to a CGH ns. The object may become k e s e s n s f e m. e s -m d d s H y e n y H t, e

Usually, whe the binary CG presented in t vignetting ef paragraphs. We can also allows us to c (b) 720x720 en the recordin GH obtained f the previous s ffect seen on Fig. 8: (a simulate the r check the relia

Fig. 9:

(a)

Fig. 7: pixels calculat

ng method is for our image section is sho this image w (a) a) 720x720 pixe reconstructed ability of the c (a) Reconstruction (a) Original im ed continuous C based on a ph e, and in Fig. wn. The reco was due to th ) els calculated bi image by app code (Fig. 9a).

n of a 720x720 p (a) Simulation mage to be encod CGH, for an im hysical mask 8b, the patter orded hologram he post-CGH inary CGH and

plying the dir . pixels CGH of n and (b) Real r ded; a 10x10pix mage dimension or a laser, the rn recorded on m is a faithful imaging mou d (b) actual patt rect transform (b a 10x10 pixels reconstruction (b) xels “Z” of 2x2mm2 _{at a} e CGH is bina n the plate by l reproduction unt and has b

(b) ern recorded on mation of the b (b) “Z” of 2x2mm a focus of 2m arized. Figure y using our rec

n of the simul been correcte n the plate binary Fresne m at 2m : e 8a represents cording set-up lated one. The ed in the nex l CGH, which s p e xt h

In Fig. 9b reconstruction CGHs do not from a binary ratio between In the presen photochromic transparent fo on the photoc worth noting maximum tra 6.1 I As described light. This me the response o during the re 30 seconds to transparency finely control that it can be power. A binary CGH the plate duri adequate exp sufficient as calculated by of mask is ob Fig. 10b give 6.2 M Figure 11 illu displayed dur areas are illu remaining ma where it is po

b is shown the n set-ups. How

well suit the y CGH are ei n the focus and

nt configuratio c plate, for an orm of the illu chromic plate, that the produ ansparency tha

Illumination l

in paragraph eans that a giv of the materia ecording, than o plot the phot

of the plate a l the transpare e rescaled with

H can easily b ing the requir

osure time fo the difference y binarizing th btained, each s the exposure Mask generat ustrates the re ring its own e uminated with asks. 20 mask ossible to iden

e reconstructed wever, the ob shape and the ither pixilated d the image si on, recording n exposure ti uminated pixe , creating for e uction of gray at can be achie law 3, the photoc ven level of tr al is not linear nks to the po tochromic plat as a function o ency of the pl h a homotheti (a (b) Exp be recorded w ed time. Whil or each of them e between the e continuous exposure tim e time for eac

tion

ecording strat exposure time h the first ma ks have been ntify all steps.

d image, ident btained image e intensity of t d or “empty” ze. 6. S a binary CGH ime large eno els. The use of each step a ne yscale CGHs eved in a gray chromic mater ransparency, i r and has to be ost-CGH cam te time respon of exposure ti late. This law ic transformat

a)

Fig. 10: (a) Illu posure time of e

with our set-up le recording a m. We decide e continuous CGH pattern me is deducted h mask. They

egy using the to reach the f asks only, wh calculated, F

tical to the sim does not com the calculated with a thin b STEPPED C H requires the ough to produ f a series of d ew degree of t

does not requ yscale CGH co

rial becomes i.e. a given lev e characterize mera. Therefor nse shown in F ime. Specifica

has been obt tion in order t

umination law o each mask when

up; it simply r a stepped CGH ed to discretiz

and stepped C with threshold d from the illu y range from 1

e example of following disc hile the most Fig. 11 shows mulated one. I mpletely look continuous C boundary (high CGH e projection o uce the full c defined binary transparency, uire longer tim

orresponds to

progressively vel of gray, co ed. Our record

re we enlight Fig. 10a. This ally, it is the i tained for a gi to obtain the r ( of the photochr n the CGH is st equires displa H, a serial of ze the CGH in CGH falls the ds ranging fro umination law min 32sec up a detail of th crete level of transparent a 7 of them w It shows the q like the origin CGH. It follow h spatial frequ of a single ma conversion of masks, which allows for ob me than record the full transp

y transparent w orresponds to ding set-up cou

tened the plat s curve, called illumination la iven light pow right illumina b) omic plate tepped in 20 lev aying it on the binary mask n 20 gray lev en below 1% om 0 to 1 in st w show in Fig to 11min 43s e 10x10 pixel transparency. areas are illum with the theore

quality of our inal image (Fi ws that reconst quencies), dep

ask set on the f the opaque h are sequenti btaining steppe ding binary C parency in the when illumina a given expo uld take imag ate, and took d illumination law that will b wer, but it has ation curve for

vels

e DMD and to has to be def vels, this numb

. Twenty bin teps of 0.05. O g. 10a. The cu sec. els “Z” CGH. We can see t minated throu etical stepped recording and ig. 7a). Binary tructed images pending on the

e DMD to the form into the ially projected ed CGHs. It is GHs since the e binary CGH. ated by visible sure time. Bu ges of the plate

images every law, gives the be followed to s been verified r another ligh

o project it on fined, with the ber of steps i ary masks are Once the seria

urve shown in

Each mask is that the darke ugh almost al d CGHs image d y s e e e d s e . e ut e y e o d ht n e s e al n s r ll e

F This method alignment of 2 consecutive 6.3 S We have bee calculated (Fi Fig. 11: Record has already b f successive m e masks is nul Stepped CGH en able, thank ig. 12a) for a 2

Fig. 12: ding strategy: de been used on masks. With l; in addition, Hs recording ks to the meth 200x200 pixe (a) 720x720 pixels etail of the CGH n phase CGH a DMD, this it is instantan hod described ls "Z" of a siz s stepped CGH, (a) ca

H and the corres

but with a lo s problem ob neous to apply d above, to g ze of 2x2mm l , of a 200x200 alculated; (b) re sponding 7 mas ow quality re bviously disap y the consecut et the CGH o located at 2m pixels “Z” of 2 corded sks out of the se esult due to cr ppears since t ive masks. on Fig. 12b. I and stepped in (b) 2x2mm at a focu erial of 20 mask critical issues the position It correspond into 20 levels. us of 2m: ks

like the good error between

ds to the CGH d n

To be sure th the real one a the contours ( right place on on the plate. Fig. 13 : Ma Figure 13 sho perfectly defi noise, but afte possible to re plate at differ CGH, and the The contrast evaluated dir transmittance CCD has bee independently turns into a contrast). It i content and st The illuminat number larger 6.4 S Figure 14 sh (paragraph 2 expected. [22 A shadow app caused by a reconstructed also depend o

hat the zones c as shown in F

(black lines) c n the real one,

agnification of

ows the preci ined. The fact er verification emove this hig

rent positions en makes the h of the CGH, rectly with th e of the transp en checked an y from the tra diffraction ef is worth notin tructure of the tion law has r than 105_{. Th}

Stepped CGH

hows the sim .2). The imag 2] pears on the u defect on the d correctly if t on the quality correspond to ig.13. It repre correspond to , while red arr

a part of the wr

ision of our r t that the patt n (both calcula gh frequency s during the e high frequenc which is clos he imaging se parent areas ov nd light intens ansparency de fficiency of th ng that higher e photoactive been verified he obtained cu Hs reconstruc mulated recon ge dimension

upper left hand e CGH plate, the most trans y of the illum

o our expectat esents a small the limit betw rows show tha

ritten CGH; wit

recording tech tern of the DM ation and mea

pattern with xposure with y pattern due sely related to et-up on the ver the transm sity has been egree. A contr he order of 7 r contrasts can units). d: the mean o urve is linear, w ction nstructed imag on the came d side of the e visible in Fig sparent areas a ination. If the

tions, the cont area of the C ween the level at even a sing th contours and hnique. Each MD is visible asurement) it h a sub-pixel d a pitch small to the DMD d o the diffracti CGH plate. mittance of the calibrated in rast equal to 5 75% of the m n be reached of each level with a standar ge and the a era is 570x57 experimentally g. 12b. Fresn are altered. Th e laser beam c tours of the th CGH, obtained l 7 and 8 in th gle mirror shif

d arrows showin

micro-mirror e on the plate has actually n dithering strate

ler than a pix disappear. ion efficiency The contrast e colored area order to have 50 was obtain maximum diff by optimizing

has been cal rd deviation o actual reconst 70 pixels, wh y reconstructe el CGHs are he image size converges ins heoretical step d with an optic e theoretical C ft is visible an

ng the high reso

is clearly ide could have b o measurable egy. The prin el. This techn

y of amplitude is calculated s measured by e a good S/N ed at 610 nm fraction efficie g the photoch culated indep f 1.4%. tructed image ich gives a p ed image, it co very sensitiv and the focus stead of being pped CGH are cal magnificat CGH and it is nd has been wr olution of the re entifiable and been a source impact. It wo nciple is to sli nique allows e holograms [ d as the ratio y the CCD. T

for all the rec (10 nm band ency (achieve hromic plate ( pendently on e using our physical size orresponds to ve to defects a s chosen for t g well collima e displayed on tion of 1:3.75 s exactly at the ritten properly corded CGH d each zone is e of additiona ould have been

ghtly shift the smoothing the [13], has been o between the The linearity o corded images dwidth), which ed for infinite (i.e. thickness pixels sample second set-up of 2x2mm as the diffraction and cannot be the calculation ated, the focus n ; e y s al n e e n e f s h e s, e p s n e n s

will be shorte interference f Fig As resulting meaning tha In order to si plane-convex distance (Fig. In order to ge disk of 200 process; we w does not look The Fresnel C 2m of the len amplitude int

er and the siz fringes probab

g. 14: Reconstru

from the sim t grayscale C imulate a pha x lens chopped . 15a). enerate a Fres pixels in diam will be then a k like as a typi CGH is calcul ns. The CGH to 20 steps. ( (b (c) Simulatio e of the imag bly due to mul

(a) uction of a 720x (a) Sim mulation, the r CGHs clearly 7. ase-like device d in annular r

snel lens, the meter (Fig. 1 able to show t ical Fresnel le lated as descri is defined in (a) b) (b) Ori on of 720x720 p ge smaller, and ltiple reflectio x720 pixels step mulation of the (b) Real re reconstructed give better re . STEPPED e, a Fresnel le rings for redu

original imag 15b) for maki the ability of ns, but still ke ibed in paragr grayscale on Fig. 15: (a) Sch iginal image to pixels stepped C d vice versa i ons in the plate

pped CGH, of a reconstruction econstruction o d image (Fig. econstructed CGH - FRE ens is designe ucing the volu

ge to be encod ing a larger o f our method t

eeps the typica raph 4, with a a circular sh (c) hematic view o be encoded; a 2 CGH, of a 200p if the laser be e itself. a 200x200 pixe from theoretica f the image . 14b) is very d images than ESNEL LEN ed, calculated, ume and mass

ded is a point object to cha to generate ef al ring feature as input, a unif ape with a siz

of a Fresnel lens 200pixels unifo pixels uniform d am is divergin (b) ls “Z” of 2x2m al CGH faithful to th binary CGH NS , realized and s of the lens w t source, but w racterize after fficient Fresne es (Fig. 15c). form disk of 2 ze of 10mm ( s orm disk disk of 2mm at

ing. Note also

mm at a focus of he original im Hs. d tested. A Fre while keeping we chose inst er the image el lenses The 2mm in diame (720 pixels), a a focus of 2m o in figure 14b f 2m

mage (Fig. 7a)

esnel lens is a g a short foca tead a uniform reconstruction obtained lens eter, located a and divided in b ), a al m n s at n

The CGH – F Fig. 16. The C written with h The reconstru Figure 17 sh (paragraph 2. produced from Note also in f The reconstr –Fresnel lens Fig. 17: Fresnel lens is CGH is stepp high accuracy ucted image m

hows the sim .2). The phys m the actual i figure 17b inte ructed image ses could be d : Reconstructio s recorded on ed into 20 lev y. Note that th might then be “ Fig. 16: R mulated recon ical size of th image of the C erference fring (Fig. 17b) is designed, rec (a) n of a 720 pixe (a) Simulat a photochrom vels and magn he CGH has a “cleaner”. Recorded CGH Magnification nstructed imag he disk is exa CGH, taking t ges probably d very faithful orded and us ls in diameter s ion of the recon

(b) Real re

mic plate with nification of di a circular shap - Fresnel lens o n of parts of the ge and the a actly 2mm in then into acco due to multipl

l to the origin sed with high

stepped CGH, o nstruction from econstruction o the method de ifferent parts pe in order to on the photochr e written CGH actual reconst diameter as e ount possible le reflections i

nal image (Fi h efficiency. ( of a 200 pixels m actual CGH – f the image escribed abov of the CGH re match perfect omic plate tructed image expected. The imperfections in the plate its

ig. 15a), mean

b)

uniform disk o Fresnel lens

ve and the resu eveals the dif tly with a Fre

e using our e simulated im

s of the record self.

ning that gra

of 2mm at a focu

ult is shown in fferent features esnel-like lens

second set-up mage has been ded hologram ayscale CGHs us of 2m n s s. p n m. s

8. CONCLUSION

Computer generated holograms are well suited for optical testing and wavefront shaping. Up to now amplitude holograms have only been recorded in binary format, and our method increases their quality by enabling the realization of stepped holograms with discrete gray levels.

We have been able to successfully record several Fresnel CGHs, with stepped and binary coding. The resolution of recorded holograms was set to 720x720 pixels to be able to project it on the functional part of the photochromic plate, up to 1x1cm2 _{size. The high optical resolution of our set-up allowed making high quality recorded CGH with the desired} grayscale properly produced. The reconstructed images using stepped holograms are very faithful to the original images without being pixilated as for binary holograms.

The next step will be to code wavefronts containing phase information. We also plan to conduct the same study on Fourier holograms as they are much faster to compute and may give better results according to preliminary simulations. Finally, we will also use our method to create beam shapers including apodizers, using the same protocol as for stepped CGHs.

ACKNOWLEDGMENTS

This work has been partly funded by the European Union FP7-OPTICON 2 program.

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