This article explains how and when to use a model glass in OpticStudio. It also describes the math behind the model glass and demonstrates the accuracy within the bounds of the Model Glass.

**Authored By Dan Hill **

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## Introduction

If a glass or material you wish to use in your design does not currently exist in OpticStudio’s Materials Catalog, there are various methods available to create this glass in the program. One of these methods is to use a model glass. The model glass is used to idealize a glass by describing the dispersion in the visible wavelength region via a few input parameters: Index of refraction, Abbe number, or partial dispersion.

This article will walk through how to use the model glass tool in OpticStudio and will discuss the theory behind it and its typical uses.

## Using the Model Glass Solve

The model glass is entered into OpticStudio as a solve type via the "Material" column in the Lens Data Editor (LDE). To activate the glass solve dialog, click on the small cell to the right of the appropriate Material cell.

Of the available glass solves, select **Solve Type: Model** from the drop-down menu.

The model glass supports three different parameters: Index *N _{d}*, Abbe

*V*, and dPgF (

_{d}*ΔP*), each of which may be used to approximate the refractive properties of your glass (we will discuss this approximation in more detail in the latter pages of this article). Notice that each of these parameters support a "Vary" checkbox. By checking this box, the desired parameters may be used as variables in optimization. OpticStudio can optimize these parameters while constraining the parameter values or the computed index values to be similar to available glasses. The details of this optimization method are not covered in this article, but you may refer to the OpticStudio Help System for more information at

_{g,F}**"The Optimize Tab (sequential ui mode)...Optimization Overview...Sequential Optimization...Optimizing Using Model Glasses**."

It is important to note that model glasses are an approximation, and there are some subtleties which you should be aware of prior to using the model glass feature in OpticStudio, including:

- What definitions OpticStudio uses to approximate the model glass
- How accurate these approximations really are
- hen and when not to use the model glass

The math behind the Model Glass

OpticStudio computes the index of a model glass by idealizing the dispersion of a glass using the index of d-light, *N _{d}* (at 0.5875618

*μm*), the Abbe number (

*V*), and a term which describes the deviation of the partial dispersion (

_{d}*ΔP*) from what is known as the Normal Line.

_{g,F}The last term, *ΔP _{g,F}*, is very important to the definition of a model glass in OpticStudio. Generally, the refractive index and Abbe number alone are insufficient characterizations of optical glass for high quality optical systems, and thus the addition of the relative partial dispersion term provides a more accurate description of its properties.

^{1}

The general relative partial dispersion, *P _{x,y}*, for the wavelengths x and y is described by the equation:

^{1}

For all glasses in OpticStudio, including the model glass, OpticStudio uses the reference wavelengths *g *(blue Mercury line at 0.4358343*μm*) and* F* (blue Hydrogen line at 0.4861327*μm*) to define the relative partial dispersion. Therefore, the relative partial dispersion becomes:

The majority of glasses (often referred to as the "normal glasses"), when plotted on a graph of *P _{x,y}* vs.

*V*, follow a linear relationship. It is this line which is referred to as the normal line, and it is essential in calculating the deviation of partial dispersion for the model glass in OpticStudio. The diagram below (courtesy of Schott, see reference [1]) plots

_{d}*P*vs. Abbe number for Schott's optical glass assortment, with the addition of the normal line.

_{g,F}The position of the normal line is determined based upon value pairs of the K7 and F2 glass types.^{1} This linear relationship of partial dispersion vs. Abbe number is approximated by the following equation:

where the Abbe number, *V _{d}* in OpticStudio is given by:

and *A _{g,F}* and

*B*are specific constants for the given relative partial dispersion.

_{g,F}As can be seen from the plot on the previous page, not all glasses are perfectly represented by the normal line, thus the partial dispersion of these glasses is not accurately predicted by the linear equation above. Instead, the difference, *ΔP _{g,F}* is used to measure the deviation of the partial dispersion along the perpendicular to the normal line. It is this value which is used to approximate the refractive index of the model glass in OpticStudio, represented by "dPgF" in the glass solve dialog.

With the three parameters entered into the model glass, OpticStudio uses a proprietary formula to estimate the index at any defined wavelength. This formula is accurate to roughly 0.0001 (the index is unit-less) for typical glasses in the visible range, and should not be used outside this wavelength range, as the model glass will no longer become an accurate representation.

Accuracy of the Model Glass

To demonstrate the accuracy within the bounds of the model glass, open the sample file attached in this article. This file includes two configurations of a single lens, one which uses a model glass and one which uses a glass (N-BK7) already included in the OpticStudio Glass Catalog database. In Configuration 2, the model glass is used to best approximate N-BK7 glass from Schott. From Schott’s website, we can find the following information about the properties of N-BK7 glass.

The highlighted parameters above are typed into the appropriate entries for the model glass in Configuration 2.

The Merit Function Editor in the current demonstration file has been constructed to demonstrate the difference in refractive index for various wavelengths between the two configurations.

Wavelengths 1 through 3 are within the visible spectrum. As you can see, the wavelength differences between the model glass and the actual N-BK7 glass are quite small (<0.0001). Wavelength 4, on the other hand, is well beyond the visible spectrum, and thus the difference in refractive index becomes much larger (a difference of ~0.008087).

Small changes in refractive index can lead to significant changes in the refraction of rays, which inherently affect the performance of an optical system. Even in the presented case, note the slight difference in the paraxial image location (as calculated using a Marginal Ray Height solve) in the two configurations. Though the index of refraction of wavelength 2 (the primary wavelength) differs only slightly between the two models, the image plane location differs by roughly 0.5 microns.

## When to use (and not use) the Model Glass

Model glasses are an approximation, although usually a good approximation in the visible range. Outside this range, however, such as in the ultraviolet or infrared, the model glass is not accurate and should not be used.

It is true that even though the model glass is a good approximation in the visible spectrum, it should NOT be used as a replacement for other methods used to create glasses in OpticStudio if the required data is available to you. In other words, if adequate dispersion data is given to you for a material, use the alternate glass modeling methods in OpticStudio because they are more accurate. However, if the information available for the glass you wish to create is limited to the three parameters, the model glass in Zemax is relatively accurate and reliable in the visible spectrum.

In monochromatic designs, the model glass may be used to represent the index of refraction for the design wavelength very easily. In this special case, the Abbe number and change in partial dispersion terms should be set to zero.

For high quality optical systems, the model glass might not be an adequate representation of the dispersion of the desired glass, and should be used with great care.

## References

- Schott AG (April 2005). TIE-29: Refractive Index and Dispersion. In Technical Information – Optics For Devices (Section 2.2). Retrieved from https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/tie-29_refractive_index_v2_us.pdf
- Schott – Glass Made of Ideas. 2005 SCHOTT North America. [Online]. September 26, 2005. Available from World Wide Web: http://www.us.schott.com/english/index.html.
- Zemax Optical Design Program User’s Guide, Zemax Development Corporation

KA-01396

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