**Two sample calculations of optical throughput are covered in this article. The purpose of these is to estimate the available monochromatic power, referred to as monochromator throughput, of a detection system. The two somewhat different examples can be adapted to many of our light sources or to luminescing samples.**

The calculation of monochromator throughput may be summarized as follows:

P_{0} = P_{i}VFE_{m}R^{4}

Where:

P_{0} = Output power in mW

P_{i} = Power incident on the slit plane in mW

V = Vignetting factor due to the slit aperture being smaller than the source image

F = (F/#_{illumination})^{2}/(F/#_{monochromator})^{2}

E_{m} = Grating efficiency

R = Reflection efficiency of one of the monochromator mirrors. The R^{4} factor implies 4 reflections.

It must be noted that only P_{i} and E_{m} have a significant variation with wavelength.

## Other Factors

Certain factors have not been considered in these examples in order to avoid further confusion. However, for some circumstances, these secondary parameters can be important. These include:

## F/Number Matchers

These are used for increasing the throughput into a monochromator and decreasing stray light, but careful consideration must be made into how they are used. The Oriel 77259 F/Number Matcher, particularly for use with fibers, has a throughput of about 75%, and effectively doubles the F/Number of the illuminating beam compared to a fiber alone.

## Source Intensity Distribution

The analysis is considerably simplified by assuming uniform rectangular Lambertian sources. Real sources do not conform to this ideal.

## Lens Losses

Fresnel reflections off the lens surfaces reduce optical power. Use anti-reflection coated lenses in critical situations. Lens aberrations preclude exact imaging. This is a significant problem with small sources and low F/# lenses, which can produce a blur circle larger than the expected source image.

## Monochromator Anamorphism

The grating in the monochromator is tilted for proper dispersion. This implies that the acceptance pyramid is actually a wavelength dependent rectangle, and the entrance slit image at the output is narrower or wider than the entrance slit, depending on grating tilt direction. This can be important for high angles of grating tilt, and in these cases different slit factor widths are needed for best performance.

## Marginal Ray Loss

A simple optical sketch shows that rays entering a slit within the acceptance cone of the monochromator but at the top and bottom of the slit, can miss the collection optics. A field lens at the entrance slit can reduce this loss.

## Polarization

Diffraction gratings exhibit complicated polarization effects. The grating is more effective for either s or p polarization. This has no impact on power throughput for an unpolarized input but the monochromatic beam which exits will be partially polarized and the degree of polarization is wavelength dependent. This phenomenon can also cause misleading artifacts in radiometry and spectral analysis.

## Example 1

Estimate the power output at 450 nm of the 77700 MS257™ monochromator installed with 0.6 mm slits and the 77742 grating using a 150 watt xenon arc lamp and 66919 light source. The 66919 source has an F/0.85 condenser. To ensure the monochromator input has been completely filled, the beam from the condenser is focused on the input slit with a 127 mm focal length lens. First, we estimate how much power reaches the slit plane. The Lens Multiplication Factor, which is stated for most Oriel light sources, helps estimate the power from the source at any wavelength.

At 450 nm, the irradiance from the 150 watt xenon lamp is 14.5 mW m^{-2} nm^{-1} at a distance of 50 cm and the Lens Conversion Factor is 0.13. Therefore, the beam from the first lens has approximately 1.9 mW nm^{-1} at 450 nm. Since the source has a rear reflector which contributes about 60% more optical throughput, the beam power is estimated as 3 mW nm^{-1}. It must be noted that the secondary focusing lens transmission is about 0.9. The arc size is 0.5 mm by 2.2 mm. It is important to note that this arc dimension produces only 60% of the total radiation. The outer regions of the arc produce the other 40%. All regions contribute to the 3 mW figure.

Following the collimated beam, the condensing optics produce a 3.9/0.85 = 4.6 magnified image of the source on the slit. The source image size is then 2.3 mm x 10.1 mm. Assuming a uniform image irradiance, the fraction of image power which passes through the slit can be found by using the vignetting factor (V). Again, since the image of the source is wider, but not taller, than the slit:

It is now estimated how much power nm^{-1} at 450nm enters the monochromator:

1.8 mW nm-1 x 0.9 x 0.26 ~ 0.42 mW nm-1

The 0.6 mm slit corresponds to a bandwidth of 2.02nm, so the power into the monochromator in this bandwidth at 450 nm is:

0.42 x 2.02 ~ 0.85 mW

The grating efficiency relative to aluminum is 0.7, so the actual efficiency is about

0.7 x 0.88 = 0.62

In the lateral configuration the light is reflected off 4 aluminized mirrors inside the monochromator. Each mirror has a reflectance of about 0.88 at 450 nm so the output should be:

0.85 mW x 0.62 x 0.884 ~ 0.47 mW

The measured value is 0.24 mW, providing an excellent agreement, given the number of simplifying assumptions.

## Example 2

Estimate the power output in a 10 nm bandwidth at 500nm of the 77250 1/8 m Monochromator using 50 W QTH lamp model 6332 with the 7340 Monochromator Illuminator. The best performance is offered by the 77298 grating blazed at 350 nm. To achieve a bandwidth of 10 nm, the slit width should be set to 1.56 mm. The first step is to estimate the amount of light collected by the mirror in the 7340 illuminator. The power density in a 10 nm bandwidth is 70 mW m^{-2}. The mirror in the illuminator is 6.35 cm x 6.35 cm at a distance of 13.3 cm from the source. The collected power is estimated using the inverse square law:

## Power Through The Entrance Slit

The collected power is mostly reflected onto the monochromator slit plane. Reflection is approximately 88% efficient. Since the slit plane is 24cm from the mirror the ratio of the source image to source size is

24/13.3 = 1.8

The source is 1.6mmx3.3mm, therefore, the image size is 2.9mmx5.9 mm. The slit size is 1.56 x 12mm. Assuming a uniform image makes calculating the fraction passing through the slit a simple geometrical calculation:

1.56/2.90 = 0.54

This factor, (1.56/2.90), is from the vignetting factor as in Example 1. The power through the slit is then:

0.88 x 0.54 x 4mW = 1.9mW

## Power Through the Monochromator

The grating efficiency is about 0.6 at 500nm, and the reflectance of each of the four mirror surfaces is about 0.88 leading to a total transmittance of:

0.82 x 0.65 x 0.88^{4} = 0.32

The calculated power output is 0.32 x 1.9mW = 0.61mW. The measured value is 0.5mW. The difference is due in part to approximations made throughout. This power diverges from the monochromator as a pyramid with half angles of 6.8°.

## About Oriel Instruments

Oriel Instruments, a Newport Corporation brand, was founded in 1969 and quickly gained a reputation as an innovative supplier of products for the making and measuring of light. Today, the Oriel brand represents industry-leading instruments, such as continuous light sources covering a broad range from UV to IR, and from low to high power.

Oriel also offers monochromators and spectrographs, as well as flexible FT-IR spectroscopy solutions, making it easy for users across many industries to build instrumentation for specific applications. Oriel is also a leader in the area of Photovoltaics, with its offering of solar simulators allowing users to simulate hours of solar radiation within a matter of minutes. Oriel continues to bring innovative products and solutions to Newport customers around the world.

This information has been sourced, reviewed and adapted from materials provided by Oriel Instruments.

For more information on this source, please visit Oriel Instruments.