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Lecture 4: Optical systems (Vignetting: m = NA/NA'. Ideal: object…
Lecture 4: Optical systems
Basic Definition
Imaging on axis: circular/ rotational symmetry
Only spherical aberration and chromatical aberrations
Finite field size, object point off-axis
Chief ray as reference
Skew ray bundles: coma and distortion
Vignetting: cone of ray bundle not circular symmetric
to distinguish: tangential and sagittal plane
Numerical Aperture and F-number
related to a conjugate object/image location
NA' = n * sin(u')
F-number: F# = f / D_EnP
Generalized F-number: effective(working) F-number
s' = f'
(1-m)
sinu' = m_P
D_EnP / ( 2
n'
f
(1-m))
object-in-infinity-case: F#eff = F#
(1-m)/m_p
m: system magnification; pupil magnification: m_p = n'* D_ExP / D_EnP
Paraxial relation: F# = 1/(2
n'
tan(u'))
Special case for small angles or sine-condition corrected systems:
F# = 1/(2*NA')
Rays in 3D
Meridional rays
Sagittal rays
Coma rays
Oblique rays
Tangential- and Sagittal Plane
Ray fan and Ray cone
Pupil Sampling: for calculation of transverse aberrations
Criteria
iso energetic rays
good boundary description
good spatial resolution
Spot artefacts: line structures are discretization effects of the sampling
Pupils:Entrance and Exit Pupil
Diaphragm in Optical systems
physical stop defines the aperture cone angle u
The entrance pupil fixes the acceptance cone in the object space
The exit pupil fixes the acceptance cone in the image space
Nested Ray Path
Optical Image formation
Sequence of pupil and image planes
Matching of location and size of image planes necessary
Matching of location and size of pupils necessary for invariance of energy density
In microscopy known as Koehler illumination
Pupil mismatch:
Bad match of pupil location: key hole effect(truncation)
Field Stop Images: Iris blades
large F#--> small aperture --> image with aperture configuration
Properties of the pupil
Transfer of energy: brightness of the image
Information transfer: Resolution of details
Image quality: aberrations due to aperture
Image perspective: perception of depth
Compound systems: matching of pupils is necessary: location and size
Pupil sphere: equidistant sine-sampling
Canonical coordinates
Aplanatic system
Sine condition fulfilled: y
n
sin(w) = y'
n'
sin(w')
Pupil has spherical shape
Normalized canonical coordinates for pupil and field
Vignetting:
m = NA/NA'.
Ideal: object plane 各处的放大率一样
实际：off-axis点NA变小
Artificial vignetting: truncation of the free area of the aperture light cone.
Natural vignetting: Decrease of brightness according to cos(w)^4 due to oblique projection of areas and changed photometric distances
Definition of the chief ray: ray through energetic centroid
Truncation of the light cone with asymmetric ray path for off-axis field points.
Intensity decrease towards the edge of the image.
Vignetting can be used to avoid uncorrectable coma aberrations in the outer field.
Effective free area with extreme aspect ratio: anamorphic resolution
Illumination fall off in the image due to vignetting at the field boundary.
Telecentricity
Special stop positions
object sided telecentricity: stop in back focal plane
Image sided telecentricity: stop in front focal plane
Both-sided telecentricity: stop in intermediate focal plane
Pupil in infinity
Chief ray parallel to the optical axis
Infinity cases
Physically impossible
Object and entrance pupil in infinity
Image and exit pupil in infinity
Examples
Relay: 4 finite
Metrology lens: ExP or EnP infinity
Lithographic: EnP and ExP infinity
Afocal zoom; Telescope; Beam expander:
Object and Image Infinity
Camera lens; Focussing lens
Object infinity
Eyepiece collimator: Image infinity
Microscopic: Image and EnP
Infinity metrology lens: Object and ExP infinity
Miscellaneous imaging aspects
Anamorphotic Imaging setup
Anamorhotic factor: F = m_s / m_t
Realization: cylindrical lenses
Transforming a circular into a rectangular image format
Astigmatism over the field of view
Anamorphotic imaging: different tangential (m_t) and sagittal (m_s) magnification
Curved object surface
Object surface: spherically bended with radius R. Image bended by R'.
R and R' are bended with the same orientation. This behavior is opposite to the curved image in the Petzval picture.
Paraxial approximation: z, z'
alpha = z' / z = - m^2
R' = - R/m