*OpTaliX ^{®}*

OpTaliX是用於計算機輔助設計光學系統，薄膜多層塗層和照明系統的綜合程式。OpTaliX提供了強大的功能，可以對幾乎任何光學系統進行概念化，設計，優化，分析，公差和記錄。

OpTaliX包括幾何和衍射分析，優化，薄膜多層分析和優化，非順序射線跡線，物理光學傳播，偏振分析，重影成像，公差分析，廣泛的製造支持，用戶定義的圖形，照明，宏等等。

OpTaliX已成功用於攝影和影像鏡頭，工業光學（擴束器，鐳射掃描儀，複製，機器視覺），太空光學，變焦光學，醫療光學，照明設備，光纖電信系統，紅外光學，X-射線光學，望遠鏡，防護鏡等等。

**為什麼要使用OpTaliX ?!**

n 高效生產率：OpTaliX®的邏輯結構，人性化圖形介面（GUI）及其一致命令介面、讓您可以快速輕鬆得到最佳結果。

n 速度：OpTaliX®是一種實現軟體代碼最佳計算效率的光學設計程式。它使用最新和最快的編譯器和軟體技術。

n 分析：從幾何和衍射分析，多重容差分析，傳輸分析，極化分析等多種分析功能中獲取您設計的最多資訊。

n 精度：OpTaliX®在整個程式中使用雙精度（64位）內部算術表示。它具有最精確的最先進的演算法，而不會影響通用性。

n 優化：OpTaliX®提供了幾種優化演算法來獲得超級設計。用於構建自定義錯誤函數的非常靈活的方法可以讓您解決幾乎任何優化問題。

n 案例設計：可以從出版刊物和專利文獻以及超過8000個目錄中開始輕鬆使用超過500種設計。

n 相容性：OpTaliX®可以簡單和其他光學設計和薄膜封裝軟體進行存取，以便您可以與他人協作或檢查設計。

n 質量：計數穩定性和準確性。在我們日常設計工作中，我們經常使用OpTaliX®進行全面測試。測試用例與代碼並行開發，beta測試在選定的客戶站點進行。

n 24小時內提醒您的問題。報告的錯誤將立即修復並提供下載。

n 經驗：OpTaliX®是由光學設計師編寫的，它在實際的鏡頭設計，光學工程和軟體開發方面擁有25年經驗。

*實際案例*

Segmented Window: Rays near the edge of the segmented window undergo multiple reflections (due to total internal reflection) between the outer surfaces of the window. They do not pass through the lens, hence, a part of the aperture is virtually obstructed. | |

Lightpipe : The ray path (i.e. order of surface intersection) changes as a function of the position of the object and of the ray direction. | |

Bubble : A spherical bubble contained in solid glass. The program automatically detects total internal reflection (TIR) condition. |

Refractive Octogon : A sequence of plano surfaces forming an octogon with a hollow internal octogon structure. The model assumes parallel rays entering at a specific angle. Exiting rays are formed by refraction and total internal reflection (TIR) at the octogon facets. |

Four obstructing aperture elements are used to simulate the effects of secondary mirror and spider in a Cassegrain telescope. | Three elliptical transmitting aperture elements were logically combined (OR operation) to simulate a multi-aperture system. | Create unusual aperture shapes by logically combining basic apertures (four rectangular apertures with appropriate offsets). |

Polygon apertures allow the definition of complex and unusual apertures. Polygons need NOT be convex and any shape is allowed as indicated in the figures below. The only condition is that they must be closed, i.e. the last vertex is the same as the first vertex. The screen shots below indicate the used area on a surface by means of ray intersection patterns on the corresponding surface.

Complex polygons with many vertices (up to 50) can also be read in from a file and directly associated to a surface.

Gradient index raytrace for radial, axial and mixed gradients. Supported profiles are : SELFOC ^{TM} radial gradientGLC (Gradient Lens Corporation) GRADIUM ^{TM} axial gradientGrinTech, Jena Linear axial gradient University of Rochester gradient Luneberg gradient Spherical gradient Maxwell's fisheye gradient |

- Linear grating
- Optical hologram, formed by interfering two beams of light,
- Computer-generated holograms (CGH) with a user specified radial symmetric phase distribution,
- Computer-generated holograms (CGH) with a user specified asymmetric (two-dimensional) phase distribution,
- ''Sweatt'' model.
**Two-Point Hologram:**

This type of holographic surface describes the interference pattern of two point sources, i.e. two spherical waves, which includes plane wavefronts as the limiting case.

Any parameter in OpTaliX may be specified for multi-configuration (zoom) systems. Fixed-focus (i.e. "non-zoomed") systems are special cases of the general multi-configuration concept. For instance, "zoomable" data are wavelength, system and surface apertures, fields, radii of curvature, axial separations, tilt and decenter values, and glass types, to name just a few. Multiple positions may be optimized simultaneously, where each position may have its own merit function. |

Zoom/multiconfiguration positions can be plotted with individual X/Y-offsets, giving full control of the plot layout. Zero offsets perfectly overlay all positions. |

Optical elements can be arranged in a regular grid, i.e. they are repeated many times at specified X/Y locations with respect to the local coordinate of a surface. Examples of array elements are (see also Figure above),

a) fresnel lens array,

b) spherical lens array,

c) GRIN rod array,

d) triangular surface array.

Array properties can be combined with any type of surface, i.e. spherical, aspheric, Fresnel, GRIN and so on.

Wavefront plot of lens array with spherical surfaces. The array extension is defined by size and shape of the aperture of the base (channel) surface. |

The annular facets are modelled exactly in OpTaliX. Thus, various depths of the annular facets in a Fresnel lens lead to different aberrations. Fresnel surfaces can be refracting, reflecting, aspheric and decentered/tilted. The may also be grouped in arrays.

Light pipes are formed by extruded surfaces and are handled by the sequential surface model. Circular or rectangular cross sections are supported. All forms may be tapered. Rectangular light pipes can also be sheared (see figure below). Violation of total internal reflection (TIR) in solid pipes is taken into account.

Global coordinates locate a surface with respect to the coordinate system of any prior surface and are particularly useful for optical systems that contain tilts and decenters. In the example to the left all lenses are globally referenced to an entrance port, whereas the scan mirror rotates with respect to a decentered pivot point. The mathematics for all the required coordinate transformations are performed by OptaliX internally. |

Spot Diagrams:Spots may be displayed vs. field, wavelength and zoom position, overlayed or separated. | |

Rim ray aberrations may be shown as transverse ray aberrations or as the optical pathlength difference. Aberrations of multi-configuration (zoom) systems are plotted on one sheet, which provides an excellent overview (no need to plot each position separately). | |

Astigmatism / Field CurvatureThe longitudinal field curvature plot yields an excellent picture of the correction of the Petzval curvature and the astigmetism. Shown for all wavelengths used in the optical system. | |

Grid Distortion:Shows the distortion of a rectangular object grid as imaged through the optical system. | |

Vignetting:The vignetting plot shows the mechanical limitation or obstruction of oblique beams. It reduces the off-axis illumination in the image. However, it also plays an important role in determining the off-axis image quality. | |

Footprint:Plots the used portion of the light beams at selected surfaces. Often used in conjunction with the vignetting analysis, since the plot shows how individual beams are truncated. | |

Secondary Spectrum:Longitudinal position of the paraxial focus as a function of wavelength, here shown for a decent apochromatic refractor lens. | |

Transmission vs. Surface:Shows the contribution of each surface to the transmission losses in an optical system. Plotted for all fields defined in the system. The plot to the left shows a system with 13 lenses (26 surfaces). Each surface contributes between 4% and 9% to the transmission loss (depending on the index of refraction of a lens). The inner lenses are anti-reflection coated while the outer lenses are not. Transmission can also be plotted against wavelength or field. |

- Wavefront aberration vs. field or wavelength,
- Diffraction point spread function (PSF)
- Encircled/ensquared energy,
- Diffraction MTF vs. field, frequency, defocus and as 2-dimensional function,
- Strehl ratio vs. field or wavelength,
- Interferogram analysis,
- Zernike wavefront fit,
- Gaussian beam analysis,
- Coupling efficiency analysis.

Diffraction Point Spread Function (PSF): The PSF is calculated by FFT from the wavefront aberration. The ray density in the pupil may be increased to improve the accuracy of the PSF. The PSF may be displayed as perspective wire-grid plot, gray-scale intensity plot, false color plot or "true" color plot.Not included in OpTaliX-LT | |

Diffraction Point Spread Function (PSF):Shown as gray-scale intensity plot. Not included in OpTaliX-LT | |

Diffraction MTF: The Diffraction Modulation Transfer Function (MTF) is computed by autocorrelation of the complex pupil function (derived from wavefront). It may be computed vs. field (as shown left), vs. spatial frequency, vs. focus position or as a 2-dimensional MTF at a given field number. MTF vs. field position is always shown for three spatial frequencies.Not included in OpTaliX-LT | |

Diffraction MTF: As shown to the left, diffraction MTF is plotted vs. spatial frequency for all specified fields.Not included in OpTaliX-LT | |

Wavefront: Plot wavefront aberration vs. fields or wavelength. Vignetting is also correctly reproduced.Not included in OpTaliX-LT | |

Strehl ratio: Plot Strehl ratio vs. field or wavelength. The parametric plot to the left shows Strehl ratio vs. wavelength for a typical apochromatic refractor lens, each curve representing a separate field point. The blue curve is on-axis while the red curve is at a semi-field diagonal of 0.5^{o}.Not included in OpTaliX-LT |

Synthetic interferograms may be computed from the system wavefront, which simulate the results obtained in an interferometric test setup. Aperture obscurations (as shown left) and vignetting are taken into account. Following a tolerance simulation, not only the theoretical interferogram but also the expected result of a real manufactured system can be obtained. The wavefront, which generates the interferogram, is shown to the right of the plot. Not included in OpTaliX-LT |

Circular aperture, illuminated by a uniform plane wave. Propagation distance z = 0. | Fresnel number = 18 |

Fresnel number = 4 | Fresnel number = 1 |

Fresnel number = 4 | Fresnel number = 1 |

The Talbot imaging phenomenon is present for periodic structures. The figure to the left shows the self imaging effect of a transmissive periodic grating in the region of Fresnel diffraction. The structure is illuminated by a plane wave. The side lobes are due to the finite extent of the grating structure. |

Input field | Full overlap of beams. Note the slight ellipticity, which is due to the rectangular "pinholes", having a 4:5 aspect ratio. |

Multi-mode step-index fiber :Browse through all modes exited. Fiber parameters are : n _{1} = 1.51,n _{2} = 1.5, r_{a} = 0.025mm, l = 1.55mm. | |

Multi-mode gradient-index fiber :Browse through the first 36 modes. Fiber parameters are: n _{1} = 1.51,n _{2} = 1.5, r_{a} = 0.025mm, l = 1.55mm.Modes shown are from (m,n) = (0,0) to (m,n) = (5,5). |

KT - | optimization, minimizes an error function by a damped-least-square (DLS) method subject to solving constraints using Lagrange multipliers and application of the Kuhn-Tucker optimality condition, |

LM - | optimization, solves a problem using a modified Levenberg-Marquardt algorithm. |

The merit function is constructed from almost any command relating to performance or construction data, thus allowing unlimited flexibility in the definition of the error function (also called a merit function). Besides minimization, boundary constraints accept logical operators like

User-defined variables and functions will allow an even broader range of constraints in optimization, for example,

Edit variables, targets and constraints comfortably in a single window. The definition of a user merit function accepts all commands relating to surface data, system data and performance data. This includes arithmetic expressions, a large number of built-in mathematical functions and lens database items as also shown in the macro examples. See below a few examples of defining merit function elements:

efl = 100 | Focal length (EFL) shall be precisely 100 mm. |

syl < 70 | Constrain system length (first surface to last surface) to less than 70 mm. |

spd f1..3 w3..4 0 | Minimize rms-spot diameter (spd) at field points 1 to 3 and wavelength numbers 3 to 4 (Target is 0). |

spd 0 | As above, minimize rms-spot diameter. Absence of field and wavelength qualifier implies all fields and wavelengths. This is one of the easiest yet powerful optimization target. |

thi s1 = [OAL] - 2*[thi s4] | Use arithmetic operators and lens database items given in [ ] brackets to define complex targets. |

bfl = sqrt(tan(2)) | Use intrinsic functions to define complex targets. |

@myfkn == [oal s1..6]-5.0 | Construct a user-defined function to be used later. |

@myfkn > 10 | Use a previously defined funtion to define a constraint in optimization. |

As an example, coupling efficiency (CEF) in a DWDM photonics system is plotted as a function of wavelength. The system in use is a SELFOC

With transmission and polarization analysis turned on, the impact of the DWDM filter characteristics on coupling efficiency is clearly reproduced:

Glass Map:Glasses from one or more glass manufacturers can be plotted vs. primary dispersion (Abbe-number) and refractive index. | |

Glass Map:Plots the glasses on a linear dispersion scale (n _{F} - n_{C}) instead of Abbe-number | |

Partial Dispersion:The partial dispersion for several wavelength regimes (VIS, NIR, MIR, TIR) can also be plotted. Plots can also be shown in terms of the Buchdahl chromatic coordinate as shown below. | |

Buchdahl Partials:Plots the dispersion characteristics of optical glasses in terms of the Buchdahl chromatic coordinate h _{1} and h_{2}. This is a further aid to selecting glasses for apochromatic designs. | |

Gradium^{TM} Profile:Plots the refractive index profile of Gradium ^{TM} glass as a function of axial position and wavelength. |

Coatings may be attached to any optical surface to perform transmission or polarization analysis on system level. The effects of coatings are also included in diffraction analysis such as MTF, PSF, coupling efficiency, etc. A library of standard coating designs (anti-reflection, high- and low-pass filters, band-pass filters, etc.) as well as the most commonly used coating materials is included.

Coating Transmissivity and Reflectivity:Coating performance may be displayed for reflection or transmission vs. wavelength, incidence angle or both. A spreadsheet coating editor allows modification of the multilayer stack. Coatings can be optimized (refined). Individual layers may be excluded from refinement. Not included in OpTaliX-LT | |

Phase Change:Plot phase change on reflection or transmission vs. wavelength. Not included in OpTaliX-LT | |

Combined plot:Plot reflection/transmission vs. wavelength and incidence angle simultaneously for any input polarization state. Angular dependencies of coating properties ("blue shift"), as shown for a band pass filter on the plot to the left, are clearly indicated.Not included in OpTaliX-LT |

Coating Target Editor :Create and edit targets used in coating optimization (refinement). Targets may be reflectivity or transmissivity in either S- or T-plane or may be specified as an average of both. Not included in OpTaliX-LT |

- Use arithmetic expressions anywhere numeric input items are expected.
- Have access to a broad range of lens parameter and performance data, which can be retrieved from the program's internal database and can be reused in arithmetic expressions.
- Access to the most common mathematical functions (sin, tan, cos, sinh, cosh, tanh, asin, acos, atan, sqrt, exp, log, log10, logn, besj0, besj1, besjn, abs, min, max, aint, anint)
- User-defined variables and functions
- Pass parameters to macros
- Include macros in other macro files and build complex tasks from elementary macros or commands.
- Loop constructs: DO - ENDDO and WHILE - ENDWHILE
- Conditional constructs: IF - ELSE - ELSEIF - ENDIF
- File and data handling: OPEN, CLOSE, READ, WRITE/PRINT

A macro is a sequence of OpTaliX commands, arithmetic expressions and database items stored in a file. Macro features can be used throughout the whole program, e.g. in the command line, in the definition of the optimization merit function and in user defined graphics. Macros can be run from either command or GUI mode.

The following examples indicate some of the macro capabilities, with increasing complexity from top to bottom. The macro "

In the sample command above, two parameters are passed to the macro. the macro may also executed (run) from the menu. Here are some commented sample entries in a macro file:

sin(r) | sine of angle in radians |

cos(r) | cosine of angle in radians |

tan(r) | tangent of angle in radians |

exp(x) | e^{x} |

log(x) | natural logarithm |

log10(x) | common logarithm |

logn(n,x) | logarithm base n |

sqrt(x) | square root |

acos(r) | arccosine |

asin(r) | arcsine |

atan(r) | arctangent |

cosh(r) | hyperbolic cosine |

sinh(r) | hyperbolic sine |

tanh(r) | hyperbolic tangent |

besj0(r) | Bessel function 1^{st} kind, order 0 |

besj1(r) | Bessel function 1^{st} kind, order 1 |

besjn(n,x) | Bessel function 1^{st} kind, order n |

aint(x) | truncate to a whole number |

anint(x) | real representation of the nearest whole number |

abs(x) | absolute value |

min(a,b) | minimum value |

max(a,b) | maximum value |

Measured surface deformation: | Computed Point Spread Function: | |

---> |

Conventional Ray Trace | Ghost Ray Trace |

Ghost Images are due to the fact that optical systems can form unintended images due to reflections between pairs of surfaces. All lens surfaces reflect light to an extent depending on the refractive index of the glass itself respectively on the type of anti-reflection coating applied to these surfaces. Light reflected from the inner surfaces of a lens will be reflected again and may form reasonably well-defined images close to the image surface. Such spurious images are called

The number of possible surface combinations (pairs) which may contribute to ghost images is

Unlike in other optical design programs, OpTaliX does not require a preselection of the most disturbing ghost surface pairs on a paraxial basis (which can be extremely misleading, if not totally wrong), nor does it require to rebuild a design for each individual ghost surface pair, writing macros, storing massive ray data to files and/or display the data with the help of external programs, as required in other software packages. OptaliX entirely avoids such tedius and inefficient work! Note that the image to the left was rendered from the scratch in about 20 minutes on a 1.7GHz Pentium machine, including all (184) surface combinations, AR-coatings and absorption effects, whereas in other programs you will need hours or days for creating and testing macros and program interfaces. |

- Flat emitting sources, with circular, elliptical or rectangular shape,
- Bitmap sources, that is, the spatial source emittance is defined in a bitmap image (e.g. photo of a source),
- Ray sources, i.e. the source emission is characterized by rays.

In addition, for all flat emitting sources and bitmap sources, the angular emission characteristics can be adjusted, including Lambertian characteristics or arbitrary cos

Sources may be arbitrarily defined in 3D-space. The number of rays traced for a specific source is unlimited.

Source defined as bitmap | Extended image using the illumination feature |

Photo taken from a Tungsten lamp | Image Analysis of Tungsten Source based on ray model (1 Mio rays) |

Photorealistic rendering of light distribution | Contour plot | Slices |

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