René L. Eriksen, Paul C. Mogensen and Jesper Glückstad, âDemonstration of ternary-phase-array illumination based on the generalised phase contrast methodâ ...
Design, development and performance evaluation of Lau based array illuminators Sumitra Singh, Santosh Rana, Shashi Prakash Optics and Laser Instrumentation Laboratory, School of Instrumentation, Devi Ahilya University, Khandwa Road, Indore-452017 INDIA ABSTRACT An array illuminator is an optical system for beam shaping. It splits an incoming laser beam into a two-dimensional array of many ‘beamlets’ for the illumination of a multitude of points or devices. Such a multiple beam-splitting system is necessary in optical data processing, optical logic devices or optically bistable devices. Such devices require these beams for imaging and switching applications. The incoherent means of array generation is preferred because it is inexpensive and does not suffer from coherent noise. In this communication, we present our investigations undertaken towards design, fabrication and performance evaluation of Lau based array illuminators. Both the finite and infinite distance Lau effect has been used to generate efficient array illuminators.
KEYWORDS Lau effect, array illuminators, self-imaging
1. INTRODUCTION Optical array generation is useful in many applications such as illuminating array of optical or optoelectronic devices, optical data processing, optical digital computing or in switching systems to energize arrays of components such as logic gates, optically bistable devices, electro optic modulators and in space communication. Optical arrays are generated by splitting incoming light beam into multiple beamlets. The generated beamlets may be either one-dimensional or twodimensional; usually two-dimensional arrays are generated. Several techniques for array generators have been proposed1. They are based on arrays of pinholes2, mirrors3, arrays of microlenses4, arrays of microtelescopes, on Fraunhofer diffraction at specially designed gratings5, phase contrast imaging6, point holograms7, on Fresnel diffraction at certain gratings8, on optical co-ordinate transformations9, on leaky waveguides.10 Recently, array illuminators using interferometric techniques have also been devised. The techniques used are based on using two Michelson interferometers in tandem11, a combination of two wedge plates12 etc. Most of the above techniques use laser as a source, resulting in relatively poor efficiency and low signal to noise ratio. Besides this it is costly to procure high energy coherent sources. Lau effect is a well known phenomenon in which high contrast fringes are obtained by using two coarse gratings illuminated by a spatially and temporally incoherent source. This effect has been studied in detail by several authors. Jahns and Lohman13 explained the Lau effect and the optical properties of the optical field behind the second grating, using diffraction theory and self-imaging approach. Gori14,and Sudol and Thompson15 based their analysis on coherence theory. Swanson and Leith16 used the grating imaging approach to explain Lau effect. All the studies mentioned above considered the case of incoherent illumination of two gratings, separated by a finite distance along the illumination direction. Hence the configuration named as a finite distance Lau effect. Patorski17 presented the fringe formation process in the Lau experiment when the separation between the gratings is infinitely large. Hence, this case corresponds to the infinite distance Lau effect. In this case the second grating is illuminated by mutually incoherent plane wavefronts from the source grating. The finite distance Lau effect has been used for several applications such as measurement of refractive index18, checking for the parallelism of transparent specimen19 and for realization of a theta decoder20, a correlator21 and a refractometer22. Recently, the infinite distance
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Lau effect has been used for measurement of temperature of gaseous flames23,realization of array illuminator24 and for testing the collimation of optical beams25. The present investigation is aimed at using the finite and infinite distance Lau effect for realization of array illuminators.
2. THEORY Most of the studies dealing with explanations and applications of Lau based set-ups have reported use of linear gratings. Bartlet and Li26 used Lau based interferometer with crossed gratings and demonstrated that the phase variations of the object can be obtained simultaneously in two perpendicular directions using it. In this section, we propose to extend the explanation of 1-D Lau based grating system explained by various authors to 2D grating system. To generate a crossed grating two identical linear gratings were placed perpendicular to each other in tandem. We assume that the resulting cross grating is transparent at an array of pinholes. The first grating G1 is illuminated by an extended light source with average wavelength λ. The pinholes in G1 act as a point sources from where spherical waves emerge. The spherical waves emitted from a typical point source S in grating G1 will create secondary light sources at points Pij (i,j=0,1,2,……..)in the second grating G2. The secondary light sources will emit spherical waves with equal phase, if the path length differs by integer multiples of λ i.e.
Fig.1: Propagation of light between the crossed source grating G1 and the grating G2
(SPij) – (SP00) = (integer) λ
(1)
This will be satisfied at points Pij, when the separation between two gratings has the value Z0 = (d2/2λ)
(2)
This condition follows a simple Pythagoras theorem under parabolical approximation. More specifically, to an arbitrary point Pij in the plane of G2, we have the path length difference. (SPij) – (SP00) = [Z02 + (P00Pi0 )2 + (P00P0j)2]1/2 – Z0 ≅ [(P00Pi0
)
2
+ (P00P0j)2]/2 Z0
= (i2 + j2 ) λ = (integer)λ
(3)
This means that for a cross grating system having the same period in two perpendicular directions, an interference pattern will appear at infinity when Eq (2) is satisfied. Functioning of the illuminator can be understood by considering the light emitted from a single pinhole S in grating G1 to be spatially coherent. It produces an interference pattern at infinity after being diffracted by grating G2. But the light
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from different pinholes in G1 is mutually spatially incoherent, so the interference pattern generated by all pinholes of G1 will add up in their intensities. Given that in registry condition is satisfied along the two perpendicular directions, the resulting pattern is of high contrast. Under the conditions for self imaging Z0 x =
nd12 nd 2 , Z0 y = 2 2λ 2λ
(4)
where, λ = average wavelength of light used. n = an integer d 1 = d 2 ; d 1 and d 2 are grating constants in x and y directions respectively. This results in generation of an array pattern at the image plane of Lau lens, which has been recorded using a CCD camera. Another array generation set up used by us to implement array generation has been the arrangement when the separation between the two crossed gratings is infinitely large. The first grating may be considered as an extended periodic light source placed at the front focal plane of the collimating lens. The second grating is illuminated by a multiple of mutually incoherent quasi-plane wavefronts. The optical field behind the second grating is treated as the superimposition of mutually incoherent Fresnel diffraction fields of this grating. Under such a condition the self-image consisting of an array of spots will be observed at a plane d2/2λ away from the second grating, where the in registry condition is satisfied. It is assumed that the period of the two gratings along the perpendicular directions is identical.
3. EXPERIMENTAL ARRANGEMENT 3.1 Finite distance Lau illuminator
Fig.2: Array generation using finite distance Lau effect
The experimental arrangement to implement array generation using finite distance Lau effect is shown in Fig. 2. The beam from extended white light source such as halogen lamp is condensed by a lens and is used to illuminate the gratings G1 and G2, which are identical and are of equal periods. Grating G1 is arranged by placing two identical linear gratings, each of pitch 0.4mm in mutually perpendicular directions in tandem. G2 is also arranged such that it is formed by two gratings of equal periods in two perpendicular directions as in G1. The gratings are properly aligned and a variable focal length system is used to focus the beam onto the phase plate of CCD.
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Fig. 3(a): Experimental result recorded via CCD camera on the experimental set up as in Fig.1 L in e P ro file 275 250 225 200 175 0
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Fig. 3(b) The line profile of intensity across the image, as recorded at the CCD plane.
The images are acquired using a PC and a image grabbing card. For image acquision the IMAQ software supplied by National Instruments was used and the results were displayed on-line via the Computer monitor. Fig. 3(a) shows the experimental result recorded via a CCD camera at the image plane. The line profile of intensity at the CCD plane is also shown in Fig 3 (b). 3.2 Infinite distance Lau illuminator
Fig.4: Array generation using infinite distance Lau effect
Fig. 4 shows the experimental arrangement for array illuminator based on infinite distance Lau effect. It consists of two identical crossed gratings G1, G2. As shown in the figure the light from halogen lamp illuminates a grating G1, placed at front focal plane of collimating lens LC. The plane wavefronts from the collimating lens illuminate the grating G2. The well defined array patterns behind the second grating called the self images or Fresnel images are observed at the
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observation plane. They are generated when the Fresnal image of grating G2 due to each opening/pinhole of grating G1 overlaps with the Fresnel images generated due to other openings/pinholes of the grating G1 on the observation plane. This happens when the separation between second grating and the observation plane is d2/2λ.
Fig. 5(a): Experimental result recorded via CCD camera on the experimental set up as in Fig. 4
L in e P ro file 300
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Fig. 5(b) The line profile of intensity across the image, as recorded at the CCD plane.
At the plane separated from G2 by 250mm is observed the array pattern. The array pattern is recorded using a CCD camera. Fig. 5(a) shows the array pattern recorded via CCD camera as per the experimental arrangement of Fig.4. Fig. 5(b) shows the line profile of intensity across the image.
4. RESULTS AND DISCUSSION To determine the quality of array generated we evaluated parameters describing their performance. Splitting ratio for both types of illuminators is determined to be 99 × 99. The homogeneity in the intensity for both the array illuminators has been found to be good. However, array spots generated using infinite distance Lau effect were more homogenous than finite distance Lau based array illuminator. Compression ratio is defined as the quotient of the bright area of the spot to the whole area of the spot pattern. It measures how well the beams of an array are separated. Compression ratio is determined to be 5 in case of infinite distance Lau illuminator and 4 in case of finite distance Lau illuminator. Back ground suppression ratio defined as the ratio between spot intensity and the background stray light present in the system, is determined to be 2.08 in finite distance Lau illuminator and 4.25 in infinite distance Lau illuminator. The two configurations studied provide for a varied choice in terms of available design options. For finite distance Lau illuminator, the separation between the two gratings has been md2/2λ; depending on various values of m (an integer) several distinct grating separations are possible. Hence the experiment can be undertaken in several observation modes. Using infinite distance Lau illuminator though the grating separation is infinite, only one observation plane is possible i.e. at the plane separated by d2/2λ from the grating G2. This restricts the operation of infinite distance Lau illuminator to
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one plane only. The attractive features of the illuminators include the ease of fabrication, and their low cost. The performance of these illuminators is better than other conventional illuminators because the image degradation due to coherent noise is minimal. The efficiency of the illuminators can further be increased if phase gratings are used instead of amplitude gratings.
5. CONCLUSIONS In summary, communication presents configurations for array illuminator based on self imaging and working in white light. The performance characteristics of the two different configurations have been studied. The array illuminators realized are inexpensive and use white light sources which are widely available. The use of incoherent light reduces coherent noise and hence improves the signal to noise ratio substantially. Also the white light interference bands have higher stability.
ACKNOWLEDGEMENT This research was performed under the research project [Grant no. 03(0938)/02/EMR-II] funded by Council of Scientific and Industrial Research (CSIR), New Delhi. Authors gratefully acknowledge the financial assistance provided by CSIR, New Delhi.
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