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Advanced calculations
Handy calculations
- diffraction
- fraunhofer diffraction
- diffraction by a circular aperture
- divergence of a diffracted plane wave
- spot size from a diffracted plane wave – observation with a lens
- diffraction by a single slit
- divergence of a diffracted plane wave
- spot size from a diffracted plane wave – observation with a lens
- diffraction by an optical system
- diffraction limit of an optical system
- power of resolution of an optical system
- grating
- generalities
- free spectral range
- miscellaneous
- littrow angle
- reflection grating
- diffracted spot shift caused by incident wave tilt-observation with a lens
- diffracted spot size and resolvance-observation with a lens
- diffracted wave divergence and resolvance
- diffracted wave tilt caused by incident wave tilt
- diffraction angle
- diffraction angle spread caused by spectral dispersion
- diffraction spot spread caused by spectral dispersion-observation with a lens
- transmission grating
- diffracted spot shift caused by incident wave tilt-observation with a lens
- diffracted spot size and resolvance-observation with a lens
- diffracted wave divergence and resolvance
- diffracted wave tilt caused by incident wave tilt
- diffraction angle
- diffraction angle spread caused by spectral dispersion
- diffraction spot spread caused by spectral dispersion-observation with a lens
- fiber optic
- fiber coupling-multimode fiber
- coupling with a single lens
- elliptical laser beam
- gaussian laser beam
- isotropic punctual source - given source position
- plane circular source - given source position
- plane circular source – given magnification
- coupling with two lenses
- elliptical laser beam – coupling with an afocal system
- gaussian laser beam
- direct coupling
- elliptical laser beam to fiber coupling
- fiber to fiber coupling
- gaussian laser beam to fiber coupling
- plane lambertian source to fiber coupling
- fiber coupling-single mode fiber
- elliptical beam
- coupling with a single lens
- coupling with two lenses - afocal system
- coupling with two lenses – general case
- direct coupling
- fiber mode radius for optimal elliptical beam coupling
- optimal fiber mode radius for given beam ellipticity
- optimal fiber mode radius for given beam waist widths
- gaussian beam
- coupling with a single lens
- coupling with two lenses
- direct coupling
- optical system for maximum coupling efficiency
- afocal system for optimal elliptical beam coupling
- single lens for optimal gaussian beam coupling
- spatial modes parameters
- cutoff wavelength
- mode radius of a single mode fiber
- number of spatial modes in a highly multimode fiber
- numerical aperture
- V number
- transmission parameters
- chromatic dispersion-single mode fiber
- fiber loss
- modal dispersion-step index fiber
- general parameters
- catalogs
- optical glass
- generic
- Hoya
- Ohara
- Schott
- theoretical
- wavelengths
- default wavelength and default wavelength range for chromatism
- geometrical optics
- aberration
- miscellaneous
- plane parrallel plate - ray shift vs angle of incidence
- spherical aberration
- plane parallel plate
- plane refracting surface
- spherical lens
- spherical lens interfacing different media
- spherical mirror - correction with a Schmidt plate
- spherical mirror with object at infinity
- spherical refracting surface
- aperture
- F-number
- numerical aperture – given aperture angle
- numerical aperture – given aperture diameter
- chromatic aberration
- axial and height chomatisms - object at infinity
- curved refracting surface
- real lens interfacing different media
- thin lens
- axial and height chomatisms – object at finite distance
- curved refracting surface
- real lens
- real lens interfacing different media
- thin lens
- miscellaneous
- achromat
- constringence
- depth of field-defocus
- miscellaneous
- depth of field of a collimating and focusing system made of two lenses
- paraxial system – general case
- depth of field and maximum defocus-object at infinity
- depth of field – object at finite distance
- maximum defocus – object at finite distance
- paraxial conjugation
- field size
- image field angle – given object field in the front focal plane
- object field size vs image field size – given focal length and image position
- image position
- curved refracting surface
- plane parallel plate
- plane refracting surface
- image position and system parameters – given magnification
- curved mirror ( given object position)
- curved refracting surface ( given distance between object and image)
- thin lens ( given distance between object and image)
- image position, magnification and numerical aperture
- afocal system
- catadioptric system
- combination of two thin lenses
- curved mirror
- curved refracting surface
- real lens
- real lens interfacing different media
- thin lens
- paraxial parameters
- focal lengths - principal planes
- catadioptric system
- mirror
- real lens
- real lens interfacing different media
- refracting surface
- thin lens
- miscellaneous
- power of an optical system
- prism
- deviation
- dispersion
- refraction-reflection
- refraction by a plane surface
- total reflection by a plane refracting surface
- rigorous stigmatism
- elliptical mirror
- mirror parameters and Weierstrass points position – given focal lengh and magnification
- distance between Weierstrass points – given small and large axis
- parabolic mirror
- focal length– given radius of curvature
- spherical refracting surface
- Weierstrass points position
- interference
- ar coating
- single layer
- optimal layer thickness vs angle of incidence
- optimal refraction index at normal incidence
- reflectivity vs all parameters
- fabry perot
- diverging wave
- angular size of interference rings
- power of resolution and phase dispersion
- radii of interference rings-observation with a lens
- plane wave
- angle of incidence for a given transmission
- refraction index for a given transmission
- spectral parameters of a Fabry Perot
- thickness for a given transmission
- transmission of a Fabry Perot
- wavelength for a given transmission
- optical coherence
- coherence length
- coherence time
- two waves interference
- air corner
- interfringe - observation perpendicularly to equiphase planes
- interfringe - observation perpendicularly to the first reflecting surface
- number of observable fringes-slightly diverging source
- interference from plane parallel plate
- angular size of equal inclination rings
- radii of equal inclination rings – observation with a lens
- michelson or similar interferometer
- Michelson – relative intensity vs optical paths difference
- Michelson – tilted mirror - number of equal thickness fringes on a given observation width
- Michelson – wavelength for given relative intensity and optical paths difference
- relative intensity vs optical path difference and reflection phase shift
- newton rings
- minimum dark ring fringe order
- radii of ring fringes
- two slits interference
- angular size of interfringe and diffraction envelope
- size of interfringe and diffraction enveloppe – observation with a lens
- laser
- beam parameters
- elliptical beam
- normalized intensity distribution
- gaussian beam
- normalized intensity distribution
- stability condition for a Fabry Perot resonator
- waist radius and position in a Fabry Perot cavity
- waist radius in a confocal cavity
- beam propagation
- elliptical beam
- beam shaping with a curved refracting surface
- beam shaping with a cylindrical lens
- beam shaping with a real lens
- beam shaping with a real lens interfacing different media
- beam shaping with a spherical mirror
- beam shaping with an afocal system
- beam shaping with two cylindrical lenses
- beam shaping with two lenses
- characteristic parameters
- real intensity distribution during propagation
- shaping with a refractive optical system
- elliptical beam - vertical and horizontal waists at different positions
- beam shaping with a cylindrical lens
- beam shaping with a single lens
- gaussian beam
- beam shaping with a curved refracting surface
- beam shaping with a cylindrical lens
- beam shaping with a lens interfacing different media
- beam shaping with a real lens
- beam shaping with a refractive optical system
- beam shaping with a spherical mirror
- beam shaping with an afocal system
- beam shaping with two thin lenses
- characteristic parameters
- depth of focus
- transmission through a circular aperture
- optical system for adapting two beams
- afocal system adapting two gaussian beams
- anamorphosing of an elliptical beam
- paraxial system adapting two gaussian beams
- power and energy
- gaussian beam
- average power density inside a given circular aperture
- pulsed laser
- average power
- duty cycle
- peak power
- spectrum and time bandwidth product
- longitudinal mode
- gap between consecutive modes
- shift of a mode induced by a change of cavity length
- time bandwidth product
- minimum pulse width - gaussian shaped light pulse
- minimum pulse width - sech2 shaped light pulse
- pulse width estimation - mode locked laser
- miscellaneous
- optical spectrum
- doppler fizeau effect
- small spectral shift converted in frequency units or in wavelength units
- optoelectronics
- acousto optic
- Bragg configuration - acousto optic as a modulator
- approximative cutoff frequency
- dynamic contrast for a given modulation frequency
- rise time
- bragg configuration - general
- bragg angle
- effect of an acoustic frequency change on the diffraction efficiency
- efficiency of an acousto optic crystal
- optimal acoustic power for maximum diffraction efficiency
- general
- quality factor
- Raman Nath configuration
- critical interaction length
- diffraction angles
- photodetection
- noise
- Johnson noise current
- photon noise
- shot noise current
- signal to noise ratio - shot noise limited photodetector – given signal current
- signal to noise ratio - shot noise limited photodetector – given optical power
- specific detectivity
- photon to electron conversion
- photocurrent induced by direct illumunitaion from a small lambertian source
- photocurrent induced by direct illumunitaion from an isotropic ponctual source
- sensitivity of a photodetector
- camera
- signal to noise ratio
- lambertian source illuminating a pixel through an optical system
- polarization
- birefringence
- birefringent material
- extraordinary refraction index vs direction of propagation
- waveplate – optical axis parallel to the facets
- optical paths difference between slow and fast axis at normal incidence
- phase shift between slow and fast axis at normal incidence
- refraction angles and phase shift order depending on incidence angle
- refraction-reflexion
- brewster angle
- reflectivity and transmission by a refracting surface
- Radiometry Photometry
- photometry
- eye sensitivity (CIE 1978 photopic)
- black body
- miscellaneous
- power density
- spectral density
- grey body
- power
- annular source
- circular source
- cylindrical source
- ratio of power emitted in a spectral range
- rectangular source
- source size for a given power
- annular source
- circular source
- cylindrical source
- rectangular source
- diffusion
- integrating sphere
- irradiance and radiance – given input power and sphere surface
- irradiance, radiance and output power – given input power and sphere diameter
- secondary source
- secondary source intensity vs received luminous flux - isotropic diffusion
- secondary source radiance vs received irradiance – diffusion with gaussian angular distribution
- secondary source radiance vs received irradiance – isotropic diffusion
- flux transmitted through an aperture
- isotropic source - circular aperture
- light source with given intensity – given aperture diameter
- punctual source with given power – given aperture diameter
- transmission for a given aperture angle
- lambertian source
- cylindrical source - rectangular aperture – given aperture angle
- plane source - circular aperture – given aperture angle
- small source - circular aperture – given aperture diameter
- flux transmitted through a light guide
- isotropic source – cylindical light guide
- lambertian circular source – cylindical light guide
- irradiance on a surface
- direct illumination
- lambertian source at infinity
- punctual source
- miscellaneous
- direct illumination vs illumination through an optical system – source at infinity
- source and screen conjugated by an optical system
- lambertian source at infinity - aperture defined with aperture diameter
- lambertian source at infinity - aperture defined with F number
- small lambertian source at finite distance - slightly opened optical system
- source in the front focal plane of an optical system
- punctual source with given intensity
- punctual source with given optical power
- small source with given radiance
- source parameters
- isotropic source
- intensity vs power
- intensity vs radiance - spherical source
- radiance vs power - spherical source
- lambertian source
- emittance vs radiance
- intensity - cylindrical source
- intensity - plane source
- optical power - cylindrical source
- optical power - plane light source
- secondary source conjugated by an optical system
- radiance of the secondary source
- miscellaneous
- element of solid angle
- solid angle defined by a cone with a circular basis
- etendue
- square source – circular angular aperture
- square source – circular aperture
- square source –rectangular aperture
- unit conversions
- geometry
- angle
- area
- distance
- pitch to spatial frequency
- spatial frequency
- photometry
- illuminance
- intensity
- luminance
- radiance to luminance conversion
- power-energy-transmission
- wavelength to electronvolt
- energy
- energy conversion
- energy in photons number
- loss or gain
- transmission
- transmission per length
- power
- power conversion
- spectrum-and-time
- frequency
- time
- wavelength to frequency
- wavelength to wave number
- thermodynamic
- pressure
- temperature