Optical Computing-Physics-Lab Report, Exercises of Physics

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Optical computing through Fourier transform

Submitted to:

Dr. Asloob Ahmed Mudassar

Submitted by:

Yasir Ali

M.Phil. Physics DPAM

PIEAS

Modern day wants fast computing. Present day computer using electronic components for computing is fast but may not meet future computing requirements. So scientists thing about a computer which works with speed of light. This type of computer is called optical computer. This computer uses Fourier transform technique to transform data into optical form for executions. Our this experiment is one part of optical computing Fourier part, i.e. studying the transformation of data to optical form.

Optical Computing:-. The concept of optical computing arose in late 1960s when NASA

faced a problem. NASA obtained pictures of moon in form of small strips. These strips were combined by other methods which degraded the quality of pictures by introducing lines at point of junction. A new technique were developed which removed the lines from the picture. This technique was called optical computing. The lines can be removed by producing Fourier transform of picture and plane waves generated by the unwanted lines can be stopped which removes the lines form picture.

Now this type of technique is used in future computer known as optical computer.

Optical computers:-:-. Common computer to us works on electricity or in others words

electronics and make use of transistors and integrated circuits based on electronics. These computers are much faster than old time vacuum tube computers but still high speed is required in modern day. So it is dreamed to make a computer which works at speed of light known as optical computer. We consider optical computers that encode data using images and compute by transforming such image.

Optical computing is numerical processing through light. Optical computing started with the design and implementation of optical systems to arbitrarily modify the complex valued spatial frequencies of an image.

Hardware for optical computing:-

1. Lasers:- Lasers are almost monochromatic light sources. LED can also be used in optical computing but only in those systems where noise is tolerated. Lasers are also used because of avoiding chromatic dispersion of light during refracting from optical components. 2. Modulators:- In optical computing image which is spatial function of spatial frequencies, is encoded in light waves. In fact light is modulated in this process. Modulation can be done by reflection and also by transmission. Modulators can be a photographic film and electro-optic, magneto-optic, and acousto-optic devices 3. Detectors:- Detectors are used to measure intensity of light signals. In fact we cannot measure phase and amplitude of a wave but we can observe it amplitude Mod square i.e. its intensity. In optical computing, detectors also have some role. 4. Lenses:- Optical computing make use of light from image. This reflected or transmitted light from image make a Fourier transform at infinity. So lenses i.e. convex lenses are used for to make Fourier transform at some finite distance. Following is a simple experiment which demonstrates some part of optical computing i.e. generation a Fourier transform.

Fourier Transform:- A mathematical tool used to solve partial differential equation. But it

has an important application in image processing. When light strikes a complicated body, then simple plane waves are generated which have different orientations. These plane waves carry information of complicated object. So we can say that a complicated object is divided into a number of simple plane waves. This phenomenon is represented by a simple Fourier transform equation.

Step 3:- Making Fourier transform of diffraction grating:- The collimated beam facilitates the formation of Fourier transform. In front of collimated beam, a grating is placed, plane waves of collimated beam strike the lines of grating and due to the phenomena of diffraction, plane waves of incident beam is divided into many plane waves making different angles with principal axis. In other words we can say that that a complex pattern of grating is divided into many simple plane waves. These plane waves carry information of grating’s structure.

We make use of another lens called Fourier transform lens whose work is indicated from its name. This lens is placed just after the grating which converges the plane waves generated by grating. As plane waves from grating are of different orientations so they on converged at different points. All these waves are converged at focal length of F.T. (Fourier transform) but only those waves having zero angle with principal axis is converged at a point on principal axis. This point is called zeroth order. Plane waves with smaller angle with principal axis are converged at two points, one above and other below to zeroth order. These points are called first orders. Similarly for larger angles third, fourth and other higher orders are formed as shown in.

Fig. Fourier Transform having different orders.

In our experiment we used F.T. lens of focal length 300mm and a screen was placed at its focal length. It was noted that intensities of all orders were maximum only at focal length of lens which should be.

The collection of all these points on screen is known as Fourier transform. The Fourier transform is formed on screen and now it is called as Fourier domain. In Fourier domain, grating is represented by frequencies called Fourier frequency.

Step 4, Measuring intensities of different orders:- we can measure intensities of different orders by photodetector. First of all a suitable detector is placed in front of F.T. lens at place where Fourier transforms is formed. But in our experiment, intensities of Fourier transforms were so large so that it saturated the current measured by detector. So we used a beam splitter

and only partial beam was allowed to make Fourier transform. But the partial beam was also intense so it saturated the current. Then we took help of polarizer. Polarizer is very efficient in reducing the intensity of beam. As intensity coming out from polarizer is dependent on angle of polarization of incident light and angle of polarization angle of polarizer, so depending on angle we can get beam of any intensity.

Polarizer helped us because the laser we used was source of plane polarized light. For zeroth and first order we adjusted large angle (=80 degree) and only then we were able to measure the intensity.

For second and third orders we changer angle to relatively smaller angles gradually and measured the intensities of those orders. The changing of angles is necessary because for one orientation of polarizer which we adjusted for zeroth order, higher orders were eliminated from F.T. screen.

Using of polarizer does not destroy the original information of intensities if Fourier frequencies. As we know that ( ), where θ is angle between plane of polarization of light and polarization axis of polarizer. Io is incident intensity on polarizer or we can say that original intensity of Fourier frequency. I is intensity measured by detector. So using this equation we can recover the original intensity of Fourier frequencies.

3. Rotating the grating also rotates the Fourier transform.
4. When we shifted the grating perpendicular to beam, then there were no changes in Fourier transform proving the shifting theorem of Fourier transform. Shifting object/grating will only change phase of light waves at Fourier screen but we can observe only intensity which is Mod Square of amplitude so shift in phase is not on observed and intensity is not changed by phase shift.
5. When we block some of incident plane waves, then Fourier transform is affected only in its intensities of Fourier frequencies. In our experiment, one side of grating were covered by tape, which blocked some portion of incident waves, this setting generated asymmetric Fourier transform.

Conclusion:- Optical computing is fast technique for computing. It is thought that it will

replace conventional computers in future because of demand of fast computing. In our simple experiment we showed that a complicated object can be transformed into a number of plane wave.