FRED version 14.40 Technical Description

1 FRED Technical Description Page 1 FRED version Technical Description Overview FRED is an advanced, surface-based optical engineering software program capable of simulating the propagation of radiation through virtually any optical/mechanical system. FRED can be applied to a very broad range of applications including but not limited to: illumination systems, lightpipes, reflectors, imaging systems, projection systems, scanners, thermal imaging systems, stray light analyses, laser and interferometric systems, ghost analyses, coherent beam propagation, prototype and experimental system layout, diagnostic analyses, and virtual prototyping. FRED is intended for everyone from the infrequent user to the experienced engineer who faces challenging real-world optical engineering problems. FRED s real-time visualization/editing and advanced user interface produce photo-realistic renderings of optical/mechanical systems with immediate user feedback.

2 FRED can accurately simulate virtually any light source including lasers, arc lamps, LEDs, ideal emitters, point sources, bulbs, user defined raysets, etc. The only limits in FRED are those of your computer s memory The user can define as many surfaces, curves, aspheric/polynomial terms, materials, coatings, wavelengths, sources, rays as the user s computer resources will allow. FRED can position any assembly, subassembly, element, surface, curve or source in the coordinate system of any other assembly, subassembly, element, surface, curve, or source. Furthermore FRED can transform any entity s coordinate system into any other coordinate system at any time. FRED s Optimum Edition offers efficient 32-CPU core capability and a hybrid optimization algorithm. Choose from built-in or user-defined merit functions, and define any number of variables and/or target surfaces; all to drive your system toward optimum performance.

3 FRED Standard Edition efficiently utilizes up to 4-CPU cores. Geometry Definition The user has many options for geometry definition ranging from direct user input of FRED primitives (lenses, mirrors, prisms, vendor elements, and surfaces/curves incorporated into user-defined custom elements), import from a CAD program, and direct import of prescription files from many lens design programs. Since FRED has a multiple document user interface, components may be cut, copied, and pasted between documents. Entities may be logically arranged into hierarchies of assemblies, subassemblies, and elements that correspond to the physical layout of the system. Each can be located relative to any arbitrary coordinate system. Any surface may be trimmed (sliced) by any implicit surface, or by an aperture collection curve, which is defined below.

4 Surface and Curve Types Surface types fall into two categories: implicit and explicit. Implicit functions define a surface through the equation f(x,y,z)=0 where all (x, y, z) points which satisfy the equation lie on the surface. Explicit functions define a surface parametrically in the form (x(u,v), y(u,v), z(u,v)) where (u,v) are the parameter values. Several explicit functions are based upon curve types described below. Implicit Surface Types: Plane (flat surface) Conicoid (spheroid, ellipsoid, hyperboloid, etc. the classic optical surface) Standard asphere (conicoid plus polynomial in even powers of radial distance) General asphere (conicoid plus polynomial in even and odd powers of radial distance) Cylinder (tube/cone) Ellipsoid/Hyperboloid (specified by two focii locations) Toroidal asphere (anamorphic aspheric potato chip surface with non-symmetric aspheric warping) XY Toroidal asphere (X or Y toroid with even/odd polynomial aspheric terms) Polynomial asphere (conicoid plus XY polynomial aspheric terms) Polynomial surface (general 3D polynomial in x, y, z) FRED Technical Description Page 2 Forbes QCon and QBsf (axially symmetric aspheres represented by Forbes polynomials) Super-Gaussians Superposition (formed from a superposition of offset and rotated super-gaussians)

5 Zernike surface (the first 66 Zernike polynomial terms plus a base conic and standard aspheric terms) User-defined surface (BASIC script) Sampled Mesh surface (Rectilinear mesh of sampled sag values with bicubic interpolation between sample points. Surface data may be imported from a bitmap file or a common ASCII INT file format) Explicit Surface Types: Tabulated cylinder (straight line extruded curve) Spline (collection of parametric polynomial patches) Ruled surface (two curves connected together) Surface of revolution (curve revolved around an arbitrary axis) NURBS surface (Non-Uniform Rational Basis-Spline surface) Trimmed parametric (explicit surface trimmed by curves in parametric space) Coil ( explicitly parameterized by coil radius, cross section radius, coil pitch and the number of turns ) Lens Modules (perfect lenses.)

6 Spherical surface, finite conjugate, infinite conjugate, afocal) Ideal Lens (perfect lens surface with f-theta, f-tan, and f-sin mapping functions) Faceted Surface (defined by a collection vertex positions and surface normals) Curve Types: Circular arc (segment of a circle or the complete circle) Conic arc (segment of a circle, ellipse, hyperbola, etc.) Line segment (single linear segment) NURBS (Non-Uniform Rational Basis-Spline curve) Spline (polynomial segments) Segmented lines (set of connected line segments user-defined, digitized or FRED-generated) Racetrack curve (rectangle with rounded corners) Composite curve (set of connected curve segments of arbitrary type) Aperture collection curve (a special collection of closed curves that may be used for surface bounding, clear aperture/edge/hole/obscuration specification, and linear extrusion) Element Primitives Commonly used geometry solids can be easily defined as Element Primitive objects.

7 A minimal set of parameters completely specifies the geometry without the need for user management of the base surfaces constructing the object. Available Element Primitives: Plane Pipe Paraboloid Circular Pyramid Parabolic Trough Hemisphere Solid Sphere Hemisphere Shell Ellipsoid Torus Cube Coil Block Wedge Rod Truncated Ellipsoid Frustum Cylinder Lens CPC Element Composites Element primitives and element composites can be combined together using Boolean operations to form complex solids. The resultant solids are dynamic, meaning that the solid is updated as its component elements are modified. Element composites are exportable to CAD from within FRED. Auxiliary Data Each surface can have any number of associated auxiliary data items. Each item consists of a name and value, and is completely user-defined and arbitrary.

8 Surface Deformations Any implicit surface type can serve as a base surface that can be deformed according to another implicit surface of the form z = f(x, y). Lens Types A lens (singlet) may be specified by radii, curvatures, or focal length/bending factor. Apertures can be circular, elliptical, or rectangular. FRED can add edges and flats as needed. By default, surfaces are spherical but may be updated to any other surface type. Mirror Types A mirror may be specified by radii, curvatures, or focal length, central thickness, material, with circular, elliptical, or FRED Technical Description Page 3 rectangular outer boundary and optional central hole. By default, surfaces are spherical/conic but may be updated to any other surface type. Prism Types A prism is specified by its dimensions and material.

9 The following prism types are supported: Abbe Amici Dove Equilateral Fresnel Rhomb Leman Pechan Penta Porro Reversion Right Angle Schmidt Corner Cube (refractive) Wedge (circular w/user-defined angle) General (user-defined angles) Cube Beamsplitter (may be dichroic, polarization, or amplitude depending upon user specification) Rectilinear Arrays Any surface, element, subassembly, or source may be replicated in a rectilinear array. Various drawing attributes of the array may be specified. Optical Coatings Bare surface with no coating Table of transmission and reflection coefficients as a function of wavelength (user-defined or digitized) Thin film layer prescription can be imported from The Essential MacCleod , Optilayer or user-defined. Table of S-state and P-state reflection/transmission coefficients as a function of wavelength and angle Polarization/waveplate model (Jones Matrix) Quarter-wave (QW single layer) User-defined Coating provides a user-defined R & T with spatial dependence.

10 Gratings/Holographic/DOE Any surface can become a grating. Assign these properties directly from the Surface dialog. Linear grating Two-point hologram w/optional aspheric phase terms Unlimited diffraction orders and efficiencies (efficiencies may be pre-computed for blazed, kinoform, binary(step), and sinusoidal grating line shapes) Continuous or modulo 2 phase additions across grating line pairs Diffraction efficiency dependence on wavelength, incident polar and azimuth angles as well as distinction between reflection and transmission efficiencies Surface Scatter Models Angle, - 0 and 3D scatter plots can be generated from single or composite scatter models. The diffuse polynomial and binomial, Harvey-Shack and ABg models can be created by the data fitting tools. Lambertian Harvey-Shack (smooth optical surface scatter) ABg (smooth optical surface scatter and others) Phong (Cosn from specular) Diffuse Black Paint (generic model) Particulates - Mie (MIL-STD-1246, uniform distribution, Gaussian distribution, IEST-STD-1246D, sampled) Diffuse polynomial (coefficients of BSDF polynomial) Diffuse binomial (coefficients of BSDF binomial) Tabulated (table of sampled values input via a file) User-defined (via a BASIC script) Tabulated PSD (table of PSD vs.)