# Introduction to Light Collection Systems

This article provides an overview of the optical systems available for research and development and helps in selecting the best optical system for your specific application. In this article general sources such as arc lamps or quartz tungsten halogen lamps are discussed. Diffraction and coherent effects are excluded.

## Total System Considerations

A system can include a source, collection optics, beam handling and processing optics, delivery optics and a detector. It is important to analyze the entire system before selecting pieces of it. The best collection optics for on application can be of limited value for another.

## F-Number and Numerical Aperture

Figure 1 shows a lens of clear aperture D, collecting light from a source and collimating it. The source is one focal length, f, from the lens.

Figure 1. Lens collecting and collimating light from a source.

The F- number is defined as:

Where:

n = Refractive index of space in which the source is located

θ = Half angle of the cone of radiation as shown in Fig. 1

Though valid only for small angles, f/D, the paraxial approximation, is widely used as F/#.

F/# ≈ f/D

## Numerical Aperture

In the world of fiber optics and microscopy, numerical aperture rather than F/#, is used to describe light gathering capability. In a medium of refractive index n, the numerical aperture is given by:

N.A. = n sin θ

The larger the N.A., the more flux is collected. In air, the maximum N.A. is 1. Microscope objectives are available with N.A. of 0.95.

N.A. and F/# are related by:

## F-Number of Mirrors

Light and focus are collected using concave spherical mirrors. The focal length of a lens can vary with wavelength due to chromatic aberration, while mirror systems are truly wideband in application.

## F-Number of Non Circular Optics

In some of the company’s products, square and rectangular mirrors were used. The F/# quoted is based on the diameter of the circle with area equal to that of the mirror. This F-number is more meaningful than that based on the diagonal when light collection efficiency is being considered.

## Collected Light and Useful Light

As light collection varies with respect to 1/(F/#)2, decreasing F/# is a simple way to maximize light collection. There is however a difference between total radiant flux collected and useful radiant flux collected. Low F/# lenses collect more flux but the lens aberrations determine the quality of the collimated output. These aberrations rapidly go up with decreasing F/#.

## Minimum practical F-Number for Lenses

The practical limit for F/# for singlet spherical lenses is based on the application. For high performance imaging, the limit is about F/4. F/2 - F/1.5 is acceptable for use as a condenser with arc lamps. The lens must be shaped properly and the correct side turned towards the source.

## Real Sources and Condensers

The key considerations in selecting and using condensers

## Transmittance

Any condensing lens material has a specific spectral transmittance range. The lens acts as a long pass filter and absorbs the visible. Oriel condensers are made from selected UV grade synthetic silica for best ultraviolet transmittance.

## Thermal Problems

Lens breakage is the most serious thermal problem in high power sources. Oriel high power Lamp Housings with F/0.7 condensers use specially mounted elements close to the source. The lamp housing fan cools the elements and the element closest to the source is always made of fused silica

## Collimation

All real sources have finite extent. Figure 2 shows some of the geometry in collecting and imaging a source. The quartz tungsten halogen lamp has a cylindrical filament of 6mm diameter by 16mm long. With the filament at the focus of an ideal 50 mm focal length condenser, the “collimated beam” in this worst case includes rays with angles from 0 to ~9° (160 mrad) to the optical axis.

Figure 2. Imperfect collimation for sources of finite size

Figure 3. a) shows the effects of spherical aberration in a single element condenser. (b) shows how moving the lens toward the source can be a useful compromise.

## Spherical Aberration

With real single element condensers, spherical aberration causes rays collected at high angle to converge even though the paraxial rays are collimated as shown in Figure 3a. The lens can be positioned as shown in Figure 3b. Oriel Condensers have focus adjust which allows you to find the best position empirically.

## Chromatic Aberration

The focal length of any lens depends on the refractive index of the lens material. Refractive index is wavelength dependent. Figure 4 shows the variation of focal length and light collection of silica lenses with wavelength.

Figure 4. The effect of refractive index variation on focal length and (1/F#)2 with wavelength for fused silica lenses. (1/F#)2 is a measure of light collection by a collimating condenser when the lens is 1 focal length from the source. Since the focal length is shorter at low wavelengths, the lens must be moved towards the source to collimate these wavelengths. When you move it closer you also collect more light.

## Achromatic Lenses

The impact of chromatic aberration are reduced by achromatic lenses. Most are designed only for the visible, and include elements cemented together with optical cement. Camera lenses and other achromats are valuable with low intensity or distant visible sources.

The company’s quartz tungsten halogen lamps have strongest irradiance normal to the plane of the filament. The lamp housings are so designed that the optical axes of the condensers lie in the direction of highest radiance.

## Mirrors, an Alternate Method

There are certain advantages that make reflective optics useful instead of lenses for some collection, focusing, and imaging applications These are:

## Mirrors Do Not Have Chromatic Aberration

As reflection takes place at the surface of these optics, the wavelength dependent index of refraction does not come into play. There is no variation in how a mirror treats different incident wavelengths. It is important to take care to choose the right mirror's reflective coating as each coating exhibits slightly varying spectral reflectance as seen in Figure 5.

Figure 5. Reflectance of an AIMgF2 coated Front Surface Reflector.

## Paraboloidal Reflectors

Radiation is collected from a source at the focal point, and it is reflected as a collimated beam parallel to the axis as seen in Figure 6.

Figure 6. Paraboloidal reflector reflects light from the focus into a collimated beam, or refocuses a collimated beam at the focus.

## Ellipsoidal Reflectors

These reflectors have two conjugate foci and light from one focus passes through the other after reflection as shown in Figure 7. Deep ellipsoids of revolution surrounding a source collect a much higher fraction of total emitted light than a spherical mirror or conventional lens system.

Figure 7. Elipsoidal reflectors reflect light from one focus to a second focus, usually external.shown in the top half of the ellipse, are all from F1 and pass through F2, the second focus of the ellipse. Rays A, B and C, in the bottom half of the ellipse are exact ray traces for rays from a point close to F1. They strike the ellipse at equivalent points to a, b and c, but do not pass through F2. For a small spot (image) at F2 you need a very small source.

## How to Maximize Light through the System

First see through the proposed system, beyond the light source and condensers, for the component which limits G and, if possible, replace it with a component with a higher G. When the limiting G has been finally fixed, it is possible to sensibly select other components, to minimize cost.

The collection optics should have a value of G that is as large as Glim. Glim determines the product of source area and collection angle. These can be traded off within the limitation of source availability and maximum collection angle. Table 1 shows the average spectral radiance of various sources.

Table 1. Average Spectral Radiance of Various Sources

Source Type Model No. Input Power Nominal Source dimensions (mm) Average Spectral Radiance* (W cm-2 sr-1 nm-1)
300 nm 400 nm 500 nm 633 nm
Quartz Tungsten Halogen 6333 100 W 4.2 x 2.3 0.0015 0.013 0.034 0.065
Xenon Arc 6253 150 W 0.5 x 2.2 0.085 0.16 0.21 0.24
3400 K Blackbody       0.0037 0.03 0.08 0.15
Sun**     1.4 x 1012 0.75 2.1 2.9 2.2
HeNe Laser 79200 2 mW*** 0.63 diameter 0 0 0 108****

Note:

* Over the nominal area. Small regions may have a higher radiance.
** Based on extraterrestrial solar radiation.
*** This is output power. Conventionally, lamps are rated by input power, lasers by output power.
**** Based on a 4 x 10-3 nm line width.

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

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