# Advanced calculations

### Introduction

**Advanced calculations** is a flexible tool enabling more complex computations than the **handy calculations** pages. It is focused on the analysis of optical systems through the "Advanced calculations/system analysis" page (later called **system analysis** page). It therefore simulates the real propagation of rays. In addition, paraxial and radiometric calculations are also available.

Almost all kind of systems are compatible for calculations. Actually, up to **22 surfaces** can be entered. Different types of surfaces can be used : spherical, conical, aspherical, toroidal, biconical, paraxial and paraxial without symmetry of revolution. The tool offers the possibility to tilt and decenter surfaces.

The aperture can be defined in different ways : numerical aperture, half angle, surface diameter and f-number. It's position is specified by a surface of the system. Alternatively, the system can be telecentric in the object space or in the image space. The use of circular and rectangular aperture/obscuration is also possible.

Up to **7** different **wavelengths** and **7** different **fields** can be employed.

In addition, radiometric calculations can be processed with various sources (including black and grey bodies) of different shapes : punctual, circular, rectangular, cylindrical and annular.

Many options are available for the calculations and the display of results. Finally, it is possible to save the actual input data in the user computer (no input data is stored on the "optical-calculation.com" server).
Various analysis features are proposed.

Among others, the possible calculations include 3D texture ray tracing, spot diagrams, ray aberrations, wave front errors, point spread functions and modulation transfer function. Additionnally, it is possible to evaluate the best position for the observation surface based on a spot size analysis.

The features also include paraxial and chromatism analysis as well as the evaluation of the transmitted power from a source.

**"System analysis"** page overview

After clicking on the "Advanced calculation/system analysis" link, the user is redirected to a page enabling to enter the number of surfaces of the system. This is the appropriate page to start with as the number of surfaces has to be defined first. Regardless the page displayed when browsing the "Advanced calculation/system analysis" tool, the same menus will always be proposed on the same line just below the header:

- "Input" menu (enabling to define input parameters),

- "output" menu (enabling to perform the calculations),

- "save/upload" (links to a page enabling to save or upload input data - only displayed if the user is logged) .

**"Input" menu**

The "input" drop-down menu includes the following list:

- "number of surfaces" (enables user to define the number of surfaces of the system),

- "surfaces parameters" (enables user to define all the parameters of the surfaces),

- "add or remove a surface" (enables user to add or remove a surface anywhere in the system),

- "aperture and fields" (enables user to define the aperture size and location as well as the fields of interest),

- "wavelengths" (enables user to define the wavelengths of interest),

- "light source" (enables user to define the light source for the radiometric calculations),

- "options" (enables user to define optional parameters for calculation and display).

**"Output" menu**

The various calculations can be carried out from four drop-down menus : "paraxial", "aberrations", "chromatism" and "radiometry". Each drop-down menu displays links to calculations and to the associated tutorials.

The "__paraxial__" menu includes the following calculations links:

- "conjugation" (calculates the paraxial conjugation and paraxial parameters),

- "aperture" (calculates the paraxial aperture in the object and image spaces).

The "__aberrations__" menu includes the following calculations links:

- "2D ray tracing" (displays the rays and system in a plane),

- "3D wire frame ray tracing" (displays the rays and the outlines of the system in 3D),

- "3D texture ray tracing" (displays the rays and the textured system in 3D),

- "one ray calculation" (calculates the propagation of a single ray),

- "spot diagram" (displays the spot diagram),

- "ray aberration" (displays the ray aberration curves),

- "encircled energy" (displays the encircled energy curve),

- "table WFE" (displays the wave front error in a table),

- "surface WFE" (displays the wave front error as a 3D surface),

- "MTF" (displays the modulation transfer function curve),

- "best focus" (calculates the best focus position for the observation surface),

- "PSF" (displays the point spread function in a table),

- "PSF cut-out" (displays the point spread function cut-out as a curve),

- "vignetting" (calculates the ratio of transmitted rays).

The "__chromatism__" menu includes the following calculations list:

- "longitudinal chromatism (displays in a curve the paraxial image position depending on a the wavelength).

The "__radiometry__" menu includes the following calculations list:

- "transmitted flux" (calculates the ratio of transmitted power).

### Input pages

Each link of the "input" drop-down menu forwards the user to an input page containing the following blocks:

- one or several **input tables** with as many validation buttons as tables,

- links to **tooltips** and to a **tutorial** on the top of each table for a better understanding and usage of the tables.

**Input tables**

The input tables are different from each other. They can include all kinds of usual cells as text cells, check boxes, selection lists and radio buttons.

Some input pages (like "surfaces parameters" or "aperture and fields") may display several input tables. The input parameters are effectively recorded if the related table is validated with the related button. In other words, it is not possible to enter input parameters in different tables and then validate the tables one after the other. Indeed, once the input parameters from a table are entered, the said table has to be validated before input parameters from another table are entered.

The maximum number of characters for the input capture depends on the input parameter and is at most **14**. Therefore, the maximum number of decimals is dependent on the input number itself and is limited to **13** for positive numbers and **12** for negative ones when using a normal notation. However, it is also possible to use the scientific notation ( for instance, it is possible to enter **1.23e-12** instead of **.000000000000123**, which would not be possible because of the limited number of characters).

**Tool tips and tutorial**

Tooltips are displayed when the user hover the mouse over the "about" and "caution" buttons. They are alternately displayed in a separate page if the user clicks on the related button. "About" is a tooltip explaining what are the different parameters of the table. "Caution" gives recommendations on how to correctly enter the parameters in the table. The "tutorial" link displays a page with more explanations about the input parameters and the way to define them.

**Order of input parameters**

The parameters of an optical system by default (actually a lens) are first automatically loaded. There is a good chance that the system to analyze will be a different one. It is then necessary to enter the input parameters in the following order:

- 1) the number of surfaces ( "number of surfaces" input link),

- 2) the mandatory surfaces parameters ( "mandatory parameters" table of the "surfaces parameters" input link),

- 3) the aperture ( "aperture" table of the "aperture and fields" input link).

Indeed, this input entry order limits the impossibility or incompatibility cases. However, while entering parameters, any impossibilities or incompatibilities are detected and an error message will appear.
The order in which the other parameters are defined is random.

### Output pages

A calculation is directly performed by clicking on the related link of the "output" drop down menu. Depending on the selected calculation, the result is displayed through a graphic, in a table or in a text.

The related tutorial can be opened by the link "tutorial" located just below the calculation link in the "output" drop down menu. The tutorial details how the calculation may be completed and gives information on the possible options that can be used.

### "Save / upload" button

It is possible to save or upload all the input parameters through the "save/upload" link at the top-right of the screen, just below the header (This button is only displayed if the user is logged in). The user is then forwarded to a new page including a "save" button on the left and a large cell with an "upload" button on the right.

For saving the input parameters, simply press the "save" button. The input parameters are then stored in the "download" folder of the user computer in a file named **optical-calculation_"login".txt**, where "**login**" is the login of the user.

For uploading input parameters, the content of a file created by the precedent process or from the "optical-calculation.com" library has to be fully copied and pasted in the "upload" cell. The "upload" button must then be clicked. The user can check that the file has been correctly uploaded by screening the different input tables.