What an Instrument Can See

Fourier Optics, Coherence and the Limits of Imaging in 18 chapters — from “The paraxial system as an operator” to “Seeing what the transfer function forbids: phase contrast and super-resolution”.

Chapters

  1. The paraxial system as an operator
    • The system matrix as an operator
    • Determinant condition and the Lagrange invariant spent
    • Conjugate condition and cardinal points between media
    • The paraxial error term for translation and refraction
    • Cardinal points of a double-Gauss lens
    • Summary
    • Problems
  2. Pupils: the aperture of a linear system
    • Pupils, entrance and exit windows
    • The exit pupil specifies the image
    • Vignetting and pupil aberration
    • Pupil matching and depth of focus
    • Numerical aperture of an oil-immersion objective
    • Summary
    • Problems
  3. Radiance, etendue and a throughput budget that is spent
    • Conservation of etendue for steep cones
    • Concentration and conservation of etendue
    • The throughput budget
    • The slit-resolution trade in a fibre-fed spectrograph
    • Detector noise, photometric conversion and mode count
    • Summary
    • Problems
  4. Aberrations: the phase written on the pupil
    • The paraxial error term on Hubble
    • The wavefront aberration function
    • The Seidel expansion and five terms
    • Chromatic aberration and the achromat
    • Zernike polynomials, rms error and the Strehl ratio
    • Graded-index media and the ray equation
    • Strehl ratio of the Hubble mirror
    • Summary
    • Problems
  5. The optical constants of a medium
    • The complex index
    • Kramers-Kronig relations from causality
    • Sellmeier equation and group velocity dispersion
    • The Drude metal and the local field
    • Scattering loss in a telecommunications fibre
    • The loss curve, explained
    • Problems
  6. The boundary as a two-port
    • Fresnel equations for s polarisation
    • The p-polarisation coefficients and Stokes relations
    • The interface matrix
    • Phase on total reflection and metal reflectance
    • Ellipsometry of an oxide film
    • Summary
    • Problems
  7. Media that are designed: plasmons, metamaterials and photonic crystals
    • The surface plasmon polariton
    • Momentum mismatch and plasmon sensing
    • Effective medium and negative refractive index
    • Characteristic matrix and photonic band structure
    • A nanobeam defect cavity
    • Summary
    • Problems
  8. Polarisation as a statistical object: coherency and Mueller matrices
    • Hermitian matrices and the Pauli basis
    • Partial polarisation and the coherency matrix
    • Degree of polarisation from eigenvalues
    • The Mueller matrix and depolarisers
    • The Poincare sphere
    • A Mueller polarimeter and physical realisability
    • Summary
    • Problems
  9. Anisotropic media: the dielectric tensor and the index ellipsoid
    • The dielectric tensor
    • Propagation eigenmodes of a direction
    • The index ellipsoid and walk-off
    • Biaxial crystals and the gyration vector
    • Stress birefringence and the compensator
    • Summary
    • Problems
  10. Modulating light: electro-optic, acousto-optic and magneto-optic devices
    • The index ellipsoid under applied fields
    • The Pockels effect and the half-wave voltage
    • The Mach-Zehnder modulator and its bandwidth
    • Acousto-optic Bragg diffraction
    • Faraday rotation and the isolator
    • Summary
    • Problems
  11. Multiple beams: the stack as a matrix and the etalon as a filter
    • The characteristic matrix of an etalon
    • Stack design
    • Linear shift-invariant systems
    • The etalon filter
    • Finesse limits of a real etalon
    • Scanning the etalon filter
    • Summary
    • Problems
  12. Scalar diffraction theory, derived
    • The Helmholtz equation
    • The Helmholtz-Kirchhoff theorem
    • Kirchhoff boundary conditions and Rayleigh-Sommerfeld
    • The Fresnel approximation and its two forms
    • The Fraunhofer transform and grating resolving power
    • The zone plate and the Talbot effect
    • A zone plate X-ray microscope
    • Summary
    • Problems
  13. The lens as a Fourier transformer
    • The angular spectrum
    • The Fourier transforming property
    • The 4f system and spatial filtering
    • Optical correlation
    • Spatial filtering of a laser beam
    • Summary
    • Problems
  14. The transfer function of an imaging system
    • The amplitude point-spread function
    • The coherent transfer function
    • The optical transfer function
    • Coherent versus incoherent imaging
    • The aberrated OTF and contrast reversal
    • Resolution as bandwidth and the noise floor
    • A measured MTF and Hubble's aberrated OTF
    • Summary
    • Problems
  15. Temporal coherence: correlation, spectrum and the interferometer
    • Stationary random processes
    • The mutual coherence function
    • The Wiener-Khinchin theorem
    • Coherence time and length
    • Fourier transform spectroscopy
    • Optical coherence tomography and source choice
    • Summary
    • Problems
  16. Spatial coherence and the van Cittert-Zernike theorem
    • Mutual intensity
    • Propagation of coherence
    • Coherence area of sunlight
    • Partially coherent imaging
    • Stellar interferometry and aperture synthesis
    • Summary
    • Problems
  17. Keeping the phase: holography, wavefront modulation and adaptive optics
    • Holographic recording
    • Off-axis holography and the coherence requirement
    • Reconstruction geometry and the spatial light modulator
    • Wavefront sensing and the adaptive optics loop
    • Phase correction on two telescopes
    • Summary
    • Problems
  18. Seeing what the transfer function forbids: phase contrast and super-resolution
    • The invisible phase object
    • Zernike phase contrast and quantitative phase imaging
    • Structured illumination
    • Localisation precision and depletion microscopy
    • The super-resolution budget
    • Summary
    • Problems