Fundamental of Optical Engineering Lecture 5

 Diffraction is any behavior of light which deviates from predictions of geometrical optics.  We are concerned about the transformations of wave from near field to far field and far field to near field.  A Guassian beam represents an example of diffraction.

 This may be called ‘Fraunhofer diffraction’.

 If we consider P A for various situations such as ◦ P A = 0 for sin(  /2) = 0 unless  /2 = 0. ◦ P A = 0 for (  ssin  / λ) = ± , ±2 , ±3  … ◦ PA = 0 for sin  = m 1 λ/s where m = ±1, ±2, ±3,...  Also,  /2  0:  Therefore, we have P A being maximum for  = 0 and P A = sP 0 /( λzL)

Intensity amplitude  /2

Determine P A vs. position on a screen 1.5 m away from a 1-dimensional aperture 5  m wide for an Ar laser beam ( λ = 488 nm). Assume that the power density incident on the aperture is 10 6 W/m 2.

 The far-field pattern from a single slit is imaged onto a screen. At a wavelength of 0.6 μm, the 3 rd minimum is separated by a distance of 2 cm from the center of the diffraction pattern. (a)At what wavelength will the 4 th minimum be displaced to that location? (b)If the distance from slit to screen is 50 cm, what is the slit width? (c)If the slit is replaced by a circular aperture of diameter equal to the slit width, what is the distance on the screen from the center of the pattern to the 1 st minimum, for λ = 0.6 μm?

 P A = 0 for  = 1.22 λ/ s ….. 1 st order  P A = 0 for  = 2.23 λ/ s ….. 2 nd order  P A = 0 for  = 3.24 λ/ s ….. 3 rd order  For diffraction behind a circular aperature, m in single-slit has to be replaced by J (1 st order Bessel-function).

 This refers to how we can distinguish or resolve 2 objects or features.  For example, case of telescope objective.

 Geometrical optics gives 2 infinitesimal dots seperated bhy a distance d  f .  For diffraction theory, those dots change to Airy disc.

 This is use for resolvable images.  It may be arbitrary but useful.  This requires that the centers of the image patterns be no nearer than the angular radius of the Airy disc.

 Geometrical optics:  Diffraction theory

 Numerical Aperture,

 The far-field pattern from a single slit is imaged onto a screen. At a wavelength of 0.6  m, the 3 rd minimum is seperated by a distance of 2 cm from the center of diffraction pattern. (a)At what wavelength will the 4 th minimum be displaced to that location? (b)If the distance from slit to screen is 50 cm, what is the slit width? (c)If the slit is replaced by a circular aperture of diameter equal to the slit width, what is the distance on the screen from the center of the pattern to the 1 st minimum for λ = 0.6  m ?

 Using the Rayleigh criterion, what is the spatial resolution of an f/2.5 lens at a wavelength of 0.63 μm?

 Consider a collimated beam incident on a screen containing a circular aperture of diameter d. Where will the image of the aperture be formed if the screen is located 6 cm to the left of a lens with f = 5 cm?

 Describe and sketch the power density profile of the image of a circular aperture with d = 20 μm, assuming parameter values given in previous examples. Repeat it with d = 0.1 μm.