《lab1-simplediffraction,fourieropticsandacousto-optics》由会员分享，可在线阅读，更多相关《lab1-simplediffraction,fourieropticsandacousto-optics（5页珍藏版）》请在金锄头文库上搜索。
1、1LAB 5 - FOURIER OPTICS FALL 2009ObjectiveWe continue our analysis of diffraction with Fourier Optics and the spatial-filtering of images. Each lab bench will have an identical setup.PRELAB 1)Determine and sketch the FTs of the following functions (you dont have to derive them, you can look these up
2、):i) (Fourier Series-dont need to sketch)Ane jn2ox nii)(Impulse Train)(x nT) niii)1 for 0xT1(Periodic Square Wave with period To 0for T1xToand duty cycle T1/T0.)2)Let fs(x) = be a sampled version of some band-limited spatial function f(x) f(x)(x nT)n and let f(x) be band-limited to B lp/mm (spatial
3、frequency). Sketch the spectrum of the signal F(x) (this can be any band-limited function) and of the sampled signal Fs(x). In order for no aliasing to occur (consult your ECE210 text if you have forgotten what aliasing is) what is the relationship between B and T? In reading the lab, where will you
4、 use this relationship? PART IFOURIER TRANSFORMDiscussionThe basic optical setup for Fourier optics will be discussed in lecture. We will examine Fourier transforms of various objects and try to predict features of an object given its transform and vice versa. We will then examine how to filter spat
5、ial frequencies in these objects. From lecture, the relationship between the spatial frequency x and the distance in the Fourier transform plane x is given by xx/(f) where is the wavelength of the laser and f is the focal length of the Fourier transform lens. Because these distances are usually smal
6、l, we will use a lens to magnify the Fourier transform. The relationship between the frequency and the distance is then given byx = Qx(1)xMfwhere M is the magnification of the lens and Q= 1/Mf is a scale factor (units m-2) that relates the distance in the output plane to the spatial frequency of the
7、 input plane. We will calibrate the transform system by determining Q and then use Q to determine the magnification M.2CalibrationDiscussionTo clearly see the transforms of objects, we will have to magnify the transform plane and then calibrate the system using Eq. (1) to find the scaling factor Q.T
8、ransform LensTransform PlaneInput Plane70cmSpatial FilterLaserViewing ScreenMagnifying LensA10cm50cmCol. Lens1)A beam of collimated light will be available for you, up to the collimating lens. Place a slide holder at the input plane and place the Fourier transform lens (see Figure above) roughly 10
9、cm from the slide holder. The distances in the image are only meant as guides, and the lenses you select may have result in a different location for the transform plane.2)Measure the approximate focal length of the magnifying lens and place it in position “A“ shown on the figure to produce a real ma
10、gnified image of the Fourier transform plane at the ruled sheet at the end of the table. Because of the calibration procedure, we do not need to determine the exact location of the Fourier transform plane to do the re-imaging.3)Place the calibrated ruled grating (fundamental frequency 250 lines per
11、inch 1m or 10 line pairs per mm) at the input plane. The grating has a transmittance function of the following formSpaceTransmittanceT1To4)Observe the spatial Fourier transform at the transform plane on the ruled paper. There should be a series of bright “dots“. Now adjust the magnifying lens (A) so
12、 that these dots are magnified and in focus at the screen at the end of the table. Rotate the grating so that the “dots“ of the Fourier transform are oriented along a line of the graph paper. These “dots“ are the Fourier components of the periodic ruled grating.35)Record the spacing between the dots
13、. The frequency this distance represents is the fundamental frequency of the Fourier series (See Prelab). For the write-up, use the distance between the Fourier components and the fundamental frequency (10 line pairs per mm) to calculate the scaling factor Q from Eq.(1). From this scaling factor, ca
14、lculate the magnification factor of the lens M. Compare this with the rough calculation of M = di/do where di is the image distance (lens to screen) and do is the object distance (from the transform plane to lens). Once you have calibrated the set-up, be careful not to move any part of it for the ex
15、periment.Experiment1)Record the number of Fourier components until the first zero of the diffraction pattern (i.e. where no dot appears). Note that this may not be an integer value. For the write-up, calculate the ratio of T1/To for the ruled grating (see figure). This ratio is the gratings duty cyc
16、le. (Hint: use the results of last problem of Prelab Question 2.) 2)Place a different grid at the input (slide #2 or #14). Record the spacing between Fourier components, and the distance to the first zero. For the write-up, use the calibration factor Q and the distance between Fourier components in the transform plane to calculate the fundamental frequency. Assuming that the system is prope
