When a material is defined in a material catalog, a "reference temperature" is also entered. The nature of this temperature is sometimes misunderstood. This article explains the correct usage of the reference temperature.
Authored By Mark Nicholson
Introduction
The reference temperature in degrees Celsius is the temperature of the air to which the relative wavelength and index data is referenced. This is usually the temperature of the material at which the data was measured, but not always. This article goes into the details of the definition of the “reference temperature” of a material.
What is the "reference temperature"?
Refractive index is a dimensionless parameter which describes the ratio of the speed of light in an optical material to the speed of light in either air or vacuum. It is usually written as:
$$n = \frac{c}{v}$$
where n is the refractive index, v is the speed of light in the material and c is the speed of light in either air of vacuum. There are two common definitions used of refractive index:
- The index of a glass relative to vacuum is called the absolute index
- The index of a glass relative to air at a specified temperature and pressure (usually 20° or 25° C and 1 Atmosphere) is called the relative index
Which definition is used is irrelevant as long as the same definition is used consistently, everywhere within the optical system. Refraction depends on the index ratio between two materials, and so it does not matter whether the absolute or relative index is used, providing that the same definition is used consistently.
OpticStudio, in common with the vast majority of the optics industry, works with the relative index definition. In OpticStudio, you can define a system temperature and pressure, such as 20 degrees C and 1.0 ATM. This tells OpticStudio that any "air" space (any surface or object where the GLASS or MATERIAL property is blank) has an index of exactly 1.0. All wavelength data is referenced to air at the system temperature and pressure.
The refractive index is generally a function of wavelength. OpticStudio uses dispersion formulas of the form n(l) = some polynomial. The formula should yield a value for n that is the index of refraction relative to air at a pressure of 1.0 at some temperature called the glass reference temperature. It doesn't matter if the actual glass as measured is cold or hot, or in vacuum, or whatever. All that matters is that the resulting index computed from the dispersion formula be relative to air at 1 atmosphere pressure at the reference temperature, and that the dispersion formula is a function of the wavelength in micrometers as measured in air with pressure = 1.0 atmospheres at the reference temperature. For the index of air, OpticStudio uses the following formula:
$$n_{air} = 1 + \frac{(n_{ref} - 1) \cdot P}{1.0 + (T - 15) \cdot (3.4785 \times 10^{-3})}$$
The refractive index is also generally a function of temperature. The variation in index is modeled using a non-linear formula following Help File: The Setup Tab...System Group (the Setup Tab)...System Explorer...Environment...Index of Refraction Computation
OpticStudio optionally allows each surface to have a surface temperature and pressure that is different from the system temperature and pressure. Once OpticStudio knows the system temperature and pressure, wavelengths, surface temperature and pressure, glass reference temperature, dispersion, and thermal variation data, OpticStudio can compute the correct relative index to use for ray tracing. The method involves the following steps:
- Scale the wavelength to air at the reference temperature of the glass and a pressure of 1.0 atmosphere.
- Compute the relative index of the glass at the reference temperature from the dispersion formula.
- Compute the index of air at the reference temperature of the glass.
- Compute the absolute index of the glass (relative to vacuum) at the reference temperature of the glass.
- Compute the change in absolute index of refraction of the glass at the surface temperature.
- Compute the index of air at the system temperature and pressure.
- Compute the index of the glass relative to the air at the system temperature and pressure.
The result, which is the index of the glass at the surface temperature and pressure relative to air at the system temperature and pressure, is what is used by OpticStudio for ray tracing.
The "Adjust Index Data to Environment" switch
OpticStudio version 16 and beyond no longer has the "Use Temperature, Pressure" checkbox on the Environment Tab of the General Data dialog. When this box was checked, the program adjusted the index data to the current environment. Since this adjustment is always correct based upon the documented way of defining dispersion data, the checkbox was considered obsolete and was removed.
Unfortunately, we became aware that at least one user had incorrectly defined the reference temperature of some custom glass data, and this change therefore altered the incorrect index data in an unexpected way. This problem will only occur if:
a) The "Use Temperature, Pressure" checkbox was off,
b) User defined dispersion data had been added that was referenced to air at 20 degrees C and 1.0 ATM (which OpticStudio uses as the reference if the checkbox is off), and
c) The user defined dispersion data incorrectly defined the glass reference temperature as the actual working temperature of the glass rather than the temperature to which the index data was referenced, which must be 20° if the checkbox is off.
In summary, if OpticStudio's own thermal adjustments were disabled, and if the reference temperature of any custom glass data was not 20 degrees, then the update that version 16 provided would return index data different than earlier versions. To maintain back compatibility with these incorrectly set up files, the checkbox has been reinstated and renamed “Adjust Index Data To Environment”.
It is recommended that this switch always be checked ON.
Warning messages will now be issued if this feature is checked OFF and the glass reference temperature does not match the surface temperature. It is strongly recommended that any such warning message be addressed and resolved.