If a glass or material you wish to use in your design does not currently exist in the ZEMAX Glass Catalog, there are various methods available to create this glass in ZEMAX.  One of these methods includes what is called a model glass.  Basically, the model glass is used to idealize a glass by describing the dispersion in the visible wavelength region via a few input parameters.

The model glass is entered into ZEMAX as a solve type via the "Glass" column in the Lens Data Editor (LDE).  To activate the glass solve dialog, right mouse click on the appropriate cell, or position the cursor over the desired Glass cell and press the "Enter" key on your keyboard.

Of the available glass solves, select Model from the available pull-down menu.



The model glass supports three different parameters: Index N_d, Abbe V_d, and Dpgf (DP_g,F), 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.  ZEMAX 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 "Optimizing glass selection" of Chapter 14 in the ZEMAX User's Guide for more information.

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 ZEMAX, including:

• what definitions ZEMAX uses to approximate the model glass
• how accurate these approximations really are
• when and when not to use the model glass

ZEMAX 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 mm), the Abbe number (V_d), and a term which describes the deviation of the partial dispersion (DP_g,F) from what is known as the Normal Line.

The last term, DP_g,F, is very important to the definition of a model glass in ZEMAX.  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 ZEMAX, including the model glass, ZEMAX uses the reference wavelengths g (blue Mercury line at 0.4358343 mm) and F (blue Hyrdrogen line at 0.4861327 mm) 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_d, 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 ZEMAX.  The diagram below (courtesy of Schott, see reference [1]) plots P_g,F vs. Abbe number for Schott's optical glass assortment, with the addition of the normal line.

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 ZEMAX is given by:

and A_g,F and B_g,F are specific constants for the given relative partial dispersion.

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, DP_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 ZEMAX, represented by "Dpgf" in the glass solve dialog.

With the three parameters entered into the model glass, ZEMAX 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.

To demonstrate the accuracy within the bounds of the model glass, please open the sample file attached on the Summary and References page of this article. 

FILE:  “Accuracy of the Model Glass.ZMX”

The attached 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 ZEMAX Glass Catalog database.

In configuration 2, the model glass is used to best approximate N-BK7 glass from Schott.  From Schott’s website, http://www.us.schott.com/optics_devices/english/products/flash/abbediagramm_flash.html, 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.

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 ZEMAX 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 ZEMAX becuase 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.

The model glass in ZEMAX can be used to idealize the dispersion of a material within the visible spectrum.  Model glasses in ZEMAX are entered as a glass solve in the Lens Data Editor, and support three input parameters: the Index N_d, Abbe V_d, and Dpgf (DP_g,F).

ZEMAX uses these three input values to approximate the dispersion you wish to create in ZEMAX.  The model glass is fairly accurate within the visible range, but should NOT be used outside the visible wavelength region.  If you are limited to the data available for the glass you wish to duplicate in ZEMAX, the model glass may be an adequate representation of the dispersion of this material. 

References

1.  Schott AG (April 2005).  TIE-29: Refractive Index and Dispersion.  In Technical Information – Optics For Devices (Section 2.2).  Retrieved from http://www.schott.com/optics_devices/english/download/tie-29_refractive_index_v2.pdf.

2.  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.

3.  ZEMAX Optical Design Program User’s Guide, ZEMAX Development Corporation