Problem 3, Suppose that after the first exposure, the object was translated by a distance Ln Suppose that the double exposure speckle photograph has been taken using the arrangement in Figure 1 below This would correspond to a distance Lt, at the image plane Suppose that the developed photograph of the pinhole pairs is placed in the input aBased on Figure 1, derive an expression for the distance the abject was translated plane the read-out system in Figure 2 below. Lumd, in terms of the distance between pinhole pairs on the image plane Laia Fourier Transforming LensF Collimated light b Calculate how far apart the pinhole pairs are from each other on the film, overall Use a wavelength of 0.633 microns. Collimated light -30cm Caleulate how far apart the pishole pairs are from each otheron the Am, in thex direction. Calculate how far apart the pinhole pairs are from each other on the film in the y direction. (Lem), and (Lein)o reectively. Calialatek waukepilele Obiect plane Input plane (pinhole pairs Laie d. Caleulate the distance that the object was translated in the x direction. Caleulate the distance that the object was translated in the y direction. Calculate the distance the object was translated overall (aad respectively The lens calculates the Fourier Transform of the input plane, and displays the ourier Transform (aka spatial frequency spectrum) at the plane,one focal length downstream of the lens e. On a carefully labeled graph with x and y axes, very picture indicating the x translation, the y translation, the direction of the overall translation vector, and the total distance translated. 50 cm maging lens Suppose that the pattern observed at the FTP is as shown in the gure below in Figure 3. Film Image plane (magaified pinhole Leles 30 cm Black red-10 mm 30 Figure 1 Problem 3, Suppose that after the first exposure, the object was translated by a distance Ln Suppose that the double exposure speckle photograph has been taken using the arrangement in Figure 1 below This would correspond to a distance Lt, at the image plane Suppose that the developed photograph of the pinhole pairs is placed in the input aBased on Figure 1, derive an expression for the distance the abject was translated plane the read-out system in Figure 2 below. Lumd, in terms of the distance between pinhole pairs on the image plane Laia Fourier Transforming LensF Collimated light b Calculate how far apart the pinhole pairs are from each other on the film, overall Use a wavelength of 0.633 microns. Collimated light -30cm Caleulate how far apart the pishole pairs are from each otheron the Am, in thex direction. Calculate how far apart the pinhole pairs are from each other on the film in the y direction. (Lem), and (Lein)o reectively. Calialatek waukepilele Obiect plane Input plane (pinhole pairs Laie d. Caleulate the distance that the object was translated in the x direction. Caleulate the distance that the object was translated in the y direction. Calculate the distance the object was translated overall (aad respectively The lens calculates the Fourier Transform of the input plane, and displays the ourier Transform (aka spatial frequency spectrum) at the plane,one focal length downstream of the lens e. On a carefully labeled graph with x and y axes, very picture indicating the x translation, the y translation, the direction of the overall translation vector, and the total distance translated. 50 cm maging lens Suppose that the pattern observed at the FTP is as shown in the gure below in Figure 3. Film Image plane (magaified pinhole Leles 30 cm Black red-10 mm 30 Figure 1