Optics

1. Introduction and structure of the course.

2. Geometrical Optics

2.1 Fermat's Principle

2.2 Lenses and Principal Planes

2.3 Compound lens systems

2.3.1 Telephoto lens

2.3.2 Wide angle lens

2.3.3 Telescope (Astronomical)

2.3.4 Telescope (Galilean)

2.3.5 Telescope (Newtonian)

2.3.6 Compound Microscope

2.4 Illumination of optical systems

3. Waves and Diffraction

3.1 Mathematical description of a wave

3.2 Interference

3.3 Phasors

3.4 Diffraction from a finite slit

3.5 Diffraction from a finite slit: phasor treatment

3.6 Diffraction in 2 dimensions

4. Fraunhofer Diffraction

4.1 Fraunhofer diffraction

4.2 Diffraction and wave propagation

5. Fourier methods in Optics

5.1 The Fresnel-Kirchoff integral as a Fourier Transform

5.2 The Convolution Theorem

5.3 Some useful Fourier transforms and convolutions

5.4 Fourier Analysis

5.5 Spatial frequencies

5.6 Abbé theory of imaging

5.7 Spatial resolution of the Compound Microscope

5.8 Diffraction effects on image brightness

6 Optical instruments and fringe localization

6.1 Division of wave-front

6.1.1 Two-slit interference, Young's Slits

6.1.2 N-slit diffraction, the diffraction grating.

6.2 Division of amplitude

6.2.1 Point source

6.2.2 Extended source

7 The diffraction grating spectrograph

7.1 Interference pattern from a diffraction grating

7.1.1 Double slit, N = 2

7.1.2 Triple slit, N = 3

7.1.3 Multiple slit, N = 4 etc.

7.2 Effect of finite slit width

7.3 Diffraction grating performance

7.3.1 The diffraction grating equation

7.3.2 Angular dispersion

7.3.3 Resolving power

7.3.4 Free Spectral Range

7.4 Blazed (reflection) gratings

7.5 Effect of slit width on resolution and illumination

8 The Michelson (Fourier Transform) Interferometer

8.1 Michelson Interferometer

8.2 Resolving Power of the Michelson Spectrometer.

8.3 The Fourier Transform spectrometer

8.4 The Wiener-Khinchine Theorem

8.5 Fringe visibility.

8.5.1 Fringe visibility and relative intensities

8.5.2 Fringe visibility, coherence and correlation

9. The Fabry-Perot interferometer

9.1 The Fabry-Perot interference pattern

9.2 Observing Fabry-Perot fringes

9.3 Finesse

9.4 The Instrument width

9.5 Free Spectral Range, FSR

9.6 Resolving Power

9.7 Practical matters

9.7.1 Designing a Fabry-Perot

9.7.2 Centre spot scanning

9.7.3 Limitations on Finesse

9.8 Instrument function and instrument width

10. Reflection at dielectric surfaces and boundaries

10.1 Electromagnetic waves at dielectric boundaries

10.2 Reflection properties of a single dielectric layer.

10.3 Multiple dielectric layers: matrix method.

10.4 High reflectance mirrors

10.5 Interference Filters

10.6 Reflection and transmission at oblique incidence

10.6.1 Reflection and transmission of p-polarized light

10.6.2 Reflection and transmission of s-polarized light

10.7 Deductions from Fresnel’s equations

10.7.1 Brewsters’ Angle

10.7.2 Phase changes on reflection

10.7.3 Total (internal) reflection and evanescent waves

11. Polarized light

11.1 Polarization states

11.1.1 Case 1: Linearly polarized light,

11.1.2 Case 2: Circularly polarized light,

11.1.3 Case 3: Elliptically polarized light.

11.2 Transformation and analysis of states of polarization

11.3 Optics of anisotropic media; birefringence.

11.4 Production and manipulation of polarized light

11.4.1 Modifying the polarization of a wave

11.4.2 Production of polarized light

11.5 Analysis of polarized light

11.6 Interference of polarized light.