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optical systems design with zemax


Sequential Ray Tracing
Lecture 2

Sequential Ray Tracing
?? Rays are traced through a pre-defined sequence

of surfaces while travelling from the object surface

to the image surface. ?? Rays hit each surface once in the order (sequence)?in which the?surfaces are defined. Particularly well-suited to imaging systems (including spectrometers). ?? Numerically fast and extremely useful for the design, optimization and tolerancing of such systems. ?? Aberrations evaluated using spot diagrams, ray fan plots, OPD plots and diffraction (MTF) calculations.
February 4, 2010 Optical Systems Design 2

Example Imaging Systems

Double Gauss lens
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Schmidt-Cassegrain telescope
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Optical Systems Design

Objectives: Lecture 2
At the end of this lecture you should:
1.? 2.?

3.? 4.? 5.?

Be able to use ZEMAX to design and optimise a simple singlet lens to specified parameters. Understand the use of meridional plane layouts, spot diagrams, and ray fan plots to evaluate performance. Design and optimise a Cassegrain reflecting telescope to specified parameters. Understand the way that conic and higher order surfaces are specified in ZEMAX. Be able to achromatise a doublet lens.

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Singlet Lens Parameters
?? Focal ratio is F/4. ?? Glass is N-BK7. ?? Focal Length = 100mm. ?? Field-Of-View = 10 degrees. ?? Wavelength =?632.8nm (HeNe). ?? Centre thickness of lens: ?2mm to 12mm . ?? Edge thickness of lens: minimum 2mm. ?? Lens should be optimized for smallest RMS spot size

averaged over the field of view at the given wavelength. ?? Object is at infinity.
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Lens Data Editor (LDE)
Surf: Type ? Comment ? Radius the type of surface (Standard, Even Asphere, Diffraction Grating, etc) an optional field for?typing in surface specific comments surface radius of curvature (the inverse of curvature) in lens units the thickness in lens units separating the vertex of the current surface to the vertex of the following surface the material type (glass, air, etc.) which separates the current surface and the next surface listed in the LDE the half-size of the surface in lens units
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? Thickness

? Glass

? Semi-Diameter
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System Settings
?? Entrance Pupil Diameter (EPD) is the diameter of

the pupil in chosen lens units as seen from object space. ?? Effective focal length (efl) is distance along optical axis from the effective refracting surface to the paraxial focus.

?? So EPD = 25mm.

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Field & Wavelength Data

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Lens Data & Solves

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Performance Evaluation

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Variables for Optimisation
??Thickness of lens ??Front radius of curvature ??Back focal distance (from Surface 2

to IMA plane)

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Default Merit function

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Final System Results

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More Optical Concepts
?? Effective Refracting Surface ?? Virtual surface at which entering and exiting rays meet. A plane for paraxial (first order) rays close to the axis. ?? Zones
?? Annular regions of constant distance from the optical

axis. Can apply to lens surfaces, stops, pupils, objects & images.

?? Paraxial rays ?? Rays close to the optical axis for which first order (linear) equations can be used for the ray transport calculations.

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More Optical Concepts

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Tangential & Sagittal Planes
?? Tangential plane is identical to the

meridional plane for an axially symmetric system. Tangential rays lie within the tangential plane. ?? Sagittal plane is orthogonal to the tangential plane and intersects it along the chief ray. All sagittal rays are skew rays. The sagittal pane changes its tilt after each surface to follow the direction of the chief ray.
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Tangential & Sagittal Planes

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Back Focal Length & Effective Focal Length
?? Back focal length (BFL) is the distance along the

optical axis from the vertex of the rear lens surface to the on-axis paraxial focus for an object at infinity. ?? Effective focal length (EFL) is the distance along the optical axis from the vertex of the effective refracting surface to the on-axis paraxial focus for an object at infinity. ?? BFL controls the longitudinal location of the focus ?? EFL controls the transverse image scale at focus
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BFL, EFL & Aberrations
Dependence With wavelength With pupil zone With field zone BFL Longitudinal chromatic aberration Spherical aberration Astigmatism & field (focal plane) curvature EFL Lateral chromatic aberration Coma Distortion

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Basic Zemax Analysis Tools
??Meridional plane cross-sectional

layout (2D) ??Spot diagrams ??Transverse ray-intercept plot
?? OPD ray fan plot ?? Field curvature plot ?? PSF (diffraction) ?? Modulation transfer funtion (MTF) ?? Encircled energy plot
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I: Layout
??Good for basic check of obvious

mistakes (e.g. data entry sign errors) ??Sanity check after optimisation e.g. excessive surface curvatures, inappropriate glass/air thicknesses, negative edge thicknesses etc ??Check on mechanical vignetting

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I: Layout

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II: Spot Diagram
??Analog of the geometrical PSF ??Shows the intersection points where

a ray bundle which fills the entrance aperture meets the image plane ??For polychromatic (white light) systems these must be generated at representative wavelengths

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II: Spot Diagram

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III: Ray Fan Plots
?? Spot diagrams give little information about which

parts of the entrance pupil particular rays pass through ?? A given ray passes through the entrance pupil at a particular height P (-1<P<+1) and intercepts the image plane at a separation Δh from the chief ray ?? Transverse ray-intercept fan plots (ray fan plots) present the transverse ray height errors Δh as a function of pupil zone height P ?? Customary to present these separately for the tangential (meridional) fan and the sagittal fan
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III: Ray Fan Plots

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III: Ray Fan Plots
?? Slope of ray fan plot reflects whether image

plane is close to focus (inside focus → positive slope and vice versa) ?? If effective refractive surface is curved or image surface is curved then ray fan plot also curved ?? Behavior close to origin reflects whether image plane is close to the paraxial focus ?? Each Seidel aberration has a characteristic appearance in the ray fan plot

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III: Ray Fan Plots

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Spherical Aberration

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Coma

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Astigmatism

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Field Curvature

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Distortion

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Longitudinal Colour

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Lateral Colour

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Glass Dispersion Curve
Dispersion:

d=587.6 nm 1=486.1 nm 2=656.3 nm [Abbé number]

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Abbé Diagram
Crown glass – low dispersion Flint glass – high dispersion Use easily available glasses when possible: BK7, LLF1, F2, SF2, SF57, SK16, KzFSN4. CaFl often used as crown. Large Δn is good. Final optimization is usually done on actual melt data.
February 4, 2010 Optical Systems Design 37

Cassegrain Telescope
?? Start with a spherical primary and

secondary ?? Adjust the radius of curvature of the secondary to put the focus just behind the primary ?? Use M-solve to locate paraxial focus ?? Make primary a parabola (K=-1) ?? Adjust conic constant on secondary to get best on-axis performance
February 4, 2010 Optical Systems Design 38

Aspheric Surfaces
?? Most optical surfaces are spherical ?? By far the easiest surfaces to manufacture using

conventional polishing techniques ?? General rotationally symmetric optical surface has departure from plane (sag) given by:

where h2=x2+y2 is the axial height, c=1/R is the surface curvature at the vertex, and k the conic constant. A,B,C,D are 4th, 6th, 8th, 10th order coeffs.
k=0 sphere
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-1<k<0 prolate

k=-1 paraboloid

k<-1 hyperboloid

k>0 oblate
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Optical Systems Design

Summary: Lecture 2
?? Sequential ray tracing is the main mode of Zemax

for the design of optical systems. ?? Zemax has a range of optimising tools to improve the performance of the basic design. ?? The major tools for assessing performance are the 2D layout, the spot diagrams and the ray fan plots. ?? All the main Seidel aberrations have characteristic forms in these plots which can be used to decide how to improve the design. ?? Careful choice of glasses is required to remove longitudinal and lateral colour effects.
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Exercises: Lecture 2
?? Investigate the performance of the Cassegrain telescope for off-axis (1 deg) field points. ?? What is the main off-axis aberration ? ?? Try to minimize this aberration by making both the primary and secondary hyperbolic. ?? Achromatise the bi-convex singlet from Lecture 1 for wavelengths of 0.55 and 0.85 ?m.
February 4, 2010 Optical Systems Design 41


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