STUDY OF MONOCHROMATIC ABERRATIONS OF TWO HOLOLENS IMAGING SYSTEM

PRESENTED BY MD . ZAHEER ANSARI

DEPT.OF APPLIED PHYSICSISMU, DHANBAD

DATE : 15-05-2008

Contents What is holography? How holograms are recorded and reconstructed? Hololens, an introduction. Theory of hololens. Two hololens imaging system. Imaging characteristics. Experimental results of the recording and reconstruction

of the hololens. Experimental results of two hololens imaging system. Recording materials for holographic recordings. Holographic development. Holographic fixations. Bleaching process in holography. Experimental developing process. Results and conclusions.

What is holography?

It is a recording of both amplitude as well as the phase of the light wave using the phenomenon of interference. Holography is a method evolved by Danish Gabor in 1947.

Difference between photography

and holography. A photograph represents a two dimensional recording of a

three dimensional scene. what is recorded is the intensity distribution that prevailed at the plane of the film when it was exposed. Here the three dimensional character ,i.e,the phase distribution is completely lost.

On the other hand holography is a method in which one not only records the amplitude but also the phase of the light wave using interferometric methods.

How holograms are recorded?

To record the phase of the light wave ,holography uses a reference wave which is combined with the light from the object called object wave.

Reconstruction of holograms

When the recorded hologram is illuminated with the reference beam, diffraction from the fringe pattern on the plate reconstructs the original object wave both in amplitude and phase. That is why the holographic

image is of 3D pattern.

Hololens, an introduction Hololens is a holographic optical element made by holographic

methods. They work by the phenomenon of diffraction. Although they work by diffraction rather than by reflection or refraction, they obey all the rules of geometrical optics, and can be used for any purpose that conventional optical elements can be used for. It is a low aberration optical element.

A hologram of a point source can be generated by the interference between a spherical waves and a plane wave or between two spherical waves. Such a hologram can be regarded as a hololens.

A two point hololens has a focal-length of defined by

1/f = (c/ 0) n 1/ R1 +1/ R2

Where R1 is the distance from the point source to the hololens vertex, R2 the distance from the second point source to the hololens vertex, n the diffracted order number, 0 the construction wavelength and c the wavelength used for reconstruction. Thus the focal length of a hololens varies linearly with wavelength.

Theory of hololenspoint

p

Recording of off-axis hololens

Reconstruction of off-axis hololens

Two hololens imaging system

Recording and playback geometry

A typical system used for imaging experiment is shown in fig.1. The

first half of the system consist of object O , and hololens HL1 , and

the second half consist of a hololens HL2 , and image plane . When

the imaging properties of the lenses are fully taken into account to achieve accurate detail in the image with respect to phase and amplitude, the distance between HL1 and HL2 is equal to f1 + f2 .

Here the angle between the two beams was 100 .

Collimated beam

HL- 1

Object beam or divergence beam

Flipping of 1800

HL-2

Focus

2f

f

fo

Fig1: shows the schematic diagrams of the hololens imaging system

The lenses were place back to obtain a plan wave front from each object point and a real point focus from a plan wave. Hololens HL1 is used in the imaging

system after being rotated though 1800 with respect to the axis perpendicular to the plan of fig.1 and illuminated by a diverging beam. The radius of curvature of the wave propagated from HL1 is given by

1 1 11

1 1 1 1

l C r oR R R R

Where is the ratio of the wave lengths used for reconstructing and recording the holograms and

1 1 1 1,C r l oR R R R

1 1 1 1, , , ando r C lR R R R are the distance of object, reference, reconstruction

and image points for lens HL1 .

Hololens HL1 is used in the imaging system after being rotated through 1800 with

respect to the axis perpendicular the plane of fig.1. The radius of curvature of the wave generated from lens HL2 is given by

2 2 2 2

1 1 1 1

l C r oR R R R

2 2 2 2for andC r l oR R R R

Where

are the distances of object, reference, reconstruction, and image points for lens HL2 . This shows that the radius of curvature of the wave

exiting lens HL2 is the same as was recorded.

2 2 2 2 2 2 2 2and ,where , , andC r l o o r C lR R R R R R R R

Imaging characteristicsTo assess the aberrations introduce by HL1 and HL2 for the conditions in

which they are fabricated and used in the imaging system according to

Champagne[16] the coefficients of spherical aberrations (S) , coma (CX , CY) ,

astigmatism (Ax , Ay , Axy) , the curvature of field (F) , and distortion (Dx, Dy)

can be written as

3 3 3 3

3 3 3 3

3 3 3 3

2 2 2 2

3 3 3 3

1 1 1 1

C o r l

C o r lx

C o r l

C o r ly

C o r l

C o r lx

C o r l

SR R R R

x x x xC

R R R R

y y y yC

R R R R

x x x xA

R R R R

2 2 2 2

3 3 3 3

3 3 3 3

C o r ly

C o r l

C C o o r r l lxy

C o r l

y y y yA

R R R R

x y x y x y x yA

R R R R

2 2 2 2 2 2 2 2

3 3 3 3

3 2 3 2 3 2 3 2

3 3 3 3

3 2 3 2 3 2 3 2

3 3 3 3

C C o o r r l l

C o r l

C C C o o o r r r l l lx

C o r l

C C C o o o r r r l l ly

C o r l

x y x y x y x yF

R R R R

x x y x x y x x y x x yD

R R R R

y y x y y x y y x y y xD

R R R R

Where , , , ,, , andC C o o r r l lx y x y x y x y

are coordinates of the points giving constructing, object, reference and reconstructed beams respectively. We see that a plane wave propagates between two hololenses , i.e.,

1lR for the first lens. Lens HL1 is constructed under the condition

10R

and played back after being rotated through 1800.Under condition

1 1 1 1 1 1, ,C r C r C rx x y y R R

, the coefficients of spherical aberration(S) , coma (Cx, Cy) , astigmatism

(Ax, Ay, Axy) , field curvature (F), and distortion(DX, Dy) becomes zero .

The reconstructed beam from the first lens, HL1 , acts as the

reconstructing beam for the second lens, HL2 ,under the conditions

The coefficients of spherical aberration, coma, astigmatism, field curvature and distortion also become zero for HL2 .

The above analysis shows that through the imaging system shown in fig.1, a point object can be imaged without any conventional aberration.

2 2 2 2

2 2 2 2

, ,

,

C r o l

o l o l

R R R R

x x y y

Experimental results of the recording and reconstruction of the hololens

1.Recording of the hololens

2.Reconstruction of the hololens from the reference beam

Experimental results of two hololens imaging system

First step

Second step

A well collimated beam from the first step:

A focus of a point object using dual hololens imaging system

Recording materials

Silver – halide materials : silver-halide recording materials for holography are interesting for many reasons. It has high sensitivity in comparison with many other materials. It can be coated on both film and glass, it can cover even very large formats, it can record both amplitude and phase holograms, and it has high resolving power and easily available. But it has some drawbacks. It is absorptive; it has inherent noise and a limited linear response.

Holographic film plate

Photographic material for holography must meet specific requirements. This is essential with very high resolving power, since the dimension of the structure of the interference pattern recorded are usually of the order of the wavelength of the light used for exposure. A high speed is also desirable to allow short exposure time.

High-speed film means that the film is very sensitive to light and we can take a picture with low intensity of light. This means physically that the grain size of the emulsion must be big and that the resolution will be low. The resolution is expressed in lines pr. millimeter.

There are a number of different types of film plates .The film plate

that are chosen in this thesis is the GEOLA, fine grain silver-halide emulsion PFG-01.

These types of film plate are made to be used with a red light emitting laser.

Film type

PFG-01

Grain size

40 nm

resolution

3000 lines per mm

Spectral sensitivity range

600 – 680 nm

Table - Film plate data

Characteristic curves:

Figure1: Spectral Sensitivity curves for VRP-M (left) and PFG-01 (right).

Figure 2: Diffraction Efficiency Curves for VRP-M and PFG-01.

Chemical development: The emulsion contains grains of AgBr in a gelatine layer,

which is usually quite hard. AgBr is transparent as is the gelatine. AgBr is ionic i.e. AgBr interacting with a photon can result in the removal of the electron

hf + Br - = Br + e –

e – + Ag+ = Ag

In general if a cluster of 4 silver atoms forms within a grain then that cluster is stable (it does not dissociate back into Ag and an electron) and if we soak the emulsion in the developer (a reducing agent) then all the grains containing clusters of 4 silver atoms will be converted entirely to opaque silver. So the spatial variation in light intensity is now converted to a spatial variation in the silver concentration.

Holographic fixation

After the developing the sensitive emulsion of AgBr is still present on

the plate in the parts unaffected by light. Therefore it is necessary to

remove it in order to get the permanent image. The negative plate

after washing is dipped in a fixer solution of sodium

Thiosulphate(hypo).It dissolves the unaffected AgBr but leaves

metallic silver unchanged. Silver thiosulphate is easily soluble and will

diffuse from the emulsion into the fixing bath.

Holographic bleaching process The conversion of amplitude holograms recorded on the silver-halide

materials into phase holograms is referred to as bleaching. It ensures high diffraction efficiency, so important for holographic images.

Bleaching converts the silver into a compound whose refractive index is different from that of Ag+Br- so now there is a spatial modulation of refractive index (a phase hologram). Bleaching can be regarded as the reverse process of development.

During the development process a silver ion is reduced to free silver and developed film appears rather dark, whereas during the bleaching process metallic silver is oxidized to silver ions. For example the action of hydroquinone (the bleaching element) on silver bromide is

C6H4(OH)2 + 2AgBr + 2OH C6H4O2 +2Ag +2Br +2HOH

The experimental developer process for the transmission holograms recorded:

In the developer process for transmission holograms, developer from NOVA was used. This developer is a black-and-white developer.

The developing process:

1. Put the film in the developer. The developing time is 5 minutes at 25oC.

2. Wash the film in flowing water for 30 seconds.

3. Put the film in fixing bath. The fixing time is 5 to 6 minutes

4. Wash the film in flowing water for 30 seconds.

5. Put the film in bleacher for 5 minutes.

6. Wash the film in flowing water until the colour from the bleacher is rinsed away.

7. Let the film stand still when it is drying.

Results and conclusions When first hololens (HL1) is illuminated by a diverging beam (called the

object beam), a parallel beam is reconstructed from it. When This reconstructed (collimated) beam is allowed to fall on a second hololens (HL2) of the same diffraction efficiency, then a converging beam is formed from this hololens at its focal plane. Here the focal lengths of the both the hololenses are

F hlolens = 63 cm

and the angle between the object beam and reference beam for the hololens recorded is

= 10 0

Thus a diffraction limited two hololens imaging system has been

recorded which has been experimentally tested by imaging an off axial point. Thus the system (Two hololenses) forms images free from all types of monochromatic aberrations.

References G. Saxby : Practical holography, pp 74-75, 1991 I. Singstad : Classical holographic technique, pp 22-25, UiB, 1993 M.Hubel, L.Solymar : Color-reflection holography: Theory and experiment,

Applied optics, Vol.30, 1991 G.Saxby: Manual of practical holography, pp 93-94, 1991 W.Lauterborn, T.Kurz, M.Wiesenfeldt : Coherent optics, Springer-verlag, pp 99-

106, 1993 Born and Wolf: Elements of the theory of diffraction, Principles of optics,

Pergamon press, 1959 H.I.Bjelkhagen: Silver-halide recording materials, pp 8-11, Springer verlag, 1993 Technical information, Diagnostics imaging systems, NDT / Holography G.L.Rogers: The design of experiments for recording and reconstructing three-

dimensional objects in coherent light (Holography), J.Sci.Instrum., Vol 43, 1966 www.holographyforum.org www.fou.uib.no www.ed.ac.uk R.R.A.Sysms and Solymar, analysis of volume holographic lenses,

J.Opt.Soc.Am., p. 179, vol.72, W.T.Welford, a vector ray tracing for hololenses,opt. commun, , 322- 323 (1975) E.B.Champagne, Non paraxial imaging, opt. soc.am. ,57, 51 – 55 (1967)

ACKNOWLEDGEMENTI take this opportunity to express my profound gratitude and thanks to Dr. A. K. NIRALA for his inspiring guidance, constant encouragement and untiring supervision throughout my work.

I wish to offer my sincere thanks to all the faculty members and staff of the Department of Applied Physics, Indian School of Mines University, Dhanbad for their necessary help and encouragement in carrying out this work.

I am also thankful to all Research Scholars and my friends for extending his helping hand whenever I was need in during this work.

Finally I want to acknowledge my deep thanks for the immense moral support and encouragement which I have received from my parents.