**This article deals with coupling Oriel light sources to Oriel monochromators, the same principles apply for collecting light from any source for analysis. Specifically, all of the collection principles covered may be applied to spectrographs as well as monochromators.**

**Table 1. **Half Angle and Solid Angle Values for Various F/# Instruments

F/# |
θ_{1/2} (degrees) |
Ω (steradians) |

2.0 |
14.48 |
0.200 |

2.2 |
13.14 |
0.164 |

2.4 |
12.02 |
0.138 |

2.6 |
11.09 |
0.117 |

2.8 |
10.29 |
0.101 |

3.0 |
9.59 |
0.088 |

3.2 |
8.99 |
0.077 |

3.4 |
8.46 |
0.068 |

3.6 |
7.98 |
0.061 |

3.8 |
7.56 |
0.055 |

4.0 |
7.18 |
0.049 |

4.2 |
6.84 |
0.045 |

4.4 |
6.52 |
0.041 |

4.6 |
6.24 |
0.037 |

4.8 |
5.98 |
0.034 |

5.0 |
5.74 |
0.031 |

## Acceptance Cone and Monochromator Optics

Figure 1 shows the optics of Oriel Instruments 77200 1/4 m monochromator. The company’s 77250 1/8 m, 77700 MS257™, and new Cornerstone™ Instruments have similar layouts. Figure 2 shows the optical equivalent of the input to the monochromator in Figure1.

It can be seen from Figure 1 and 2 that the monochromator has an acceptance pyramid, often described by an F/#. The pyramid is determined by the position and dimensions of the internal optics. The optical equivalent is a grating image located behind the slit as shown in Figure 2. Only light passing through the slit in the direction of this grating image is useful.

The pyramid is normally treated as an acceptance cone with the cone peak on the center of the slit, and the F/# defined by an equivalent circle on the square grating image. The "equivalent circle" is the circle having the same area as its corresponding square; this definition results in a more accurate F/# approximation than using either the inscribed or exscribed circle. Based on the equivalent, the 77200 1/4 m has an acceptance cone with half angle of 6.4°. The half angle for the 77250 1/8 m is 7.7° and the MS257™ is 7.4°. The new Cornerstone™ 130 and 260™ Monochromators have an acceptance cone with half angle of 7.7° and 7.4° as well.

**Figure 1. **The optics of the 77200 1/4 m Monochromator.

**Figure 2. **The optical equivalent of the slit, first mirror and grating of the 77200.

## Relevance of Monochromator F/Number

Oriel Instruments 77250 and 77200 Monochromators emphasize how geometrical extent is a better measure of throughput than F/#. The 77250 has an effective F/# of 3.7, and the 77200, F/4.4. However, F/# is only the sole criterion when comparing monochromators of equivalent slit area.

## Entrance Slit Imaged on the Exit Slit

Light striking the grating is dispersed so that each wavelength leaves the grating at its appropriate angle. A small range of wavelengths leave the grating at the correct angle to pass through the exit slit. For low grating angles the imaging is often effectively 1:1, however this varies from instrument to instrument. MS257™ has 110% magnification through the system.

## Optimizing a Given Monochromator

## Grating

The most efficient grating must be selected and the slit size of any monochromator optimized for the highest throughput.

The grating blaze wavelength is a good guide. When working with a broad spectral range choose a grating that compensates for other system inefficiencies. Figure 3 shows the relative efficiency of two of Oriel Instrument gratings. The grating blazed at 750nm is obviously better above 500nm, while the 250nm blaze grating is superior in the ultraviolet.

**Figure 3. **Efficiency of two 600 l/mm gratings.

## Slit Width

The slit width is usually selected to achieve the bandpass or spectral resolution required. To optimize throughput, always use the widest slits you can, while maintaining your other system requirements. The effect of increasing the slit width depends on the source image in the slit plane and the source spectrum.

If the source image on the input slit is large and uniform, then doubling the width of both slits gives about four times as much radiation into the monochromator for a broadband source with a flat spectral distribution.

Figure 4 shows the measured variation of power through the 77250 1/8 m Monochromator against slit width, at 500 nm, for the 6333 100 W QTH lamp. An F/1.5 condenser was used to collect the light and the beam was focused on the monochromator at F/4.5, so the source image on the slit measured 6.9 by 12.6 mm, overfilling the widest slit.

**Figure 4. **(a) The variation of measured power with slit width using the 77250 Monochromator at 500 nm with a 500 nm blaze grating. Light from the 6333 100 W QTH Lamp in the Series Q Housing was focused on the input slit with a 150 mm focal length lens. Curve (b) shows an ideal relationship of power varying as slit width squared.

## Slit Height

Use the longest slits possible when the source image in slit plane is long. Long slits give more throughput for a long source image on the slit. With the light from the model 6269 kW xenon lamp collected at F/1 and imaged at F/5, the arc image on the slit is about 16 mm tall. The 18 mm fixed slits of the 77200 give 30% more power through the 77200 than 12 mm slits on the Multiple Slit Wheel.

## Size of the Radiating Element

The size of the primary radiating element is crucial to the choice of input optics.

## Case I - Large Radiating Area

A large uniformly emitting source may fill the base of the acceptance cone. Input optics will not increase the radiation through the monochromator, nor will moving the monochromator towards or away from the radiating area, providing the area continues to fill the base of the cone. In order to get the most radiation through, use the largest slits possible.

## Case II - "Point Source" (or Lasers)

The theoretical point source does not exist, but some very small fiber optic sources, pinhole images and laser sources (or laser induced radiation) may approximate a point source of radiation. For the point source approximation, any magnified image of the radiating source should underfill the slit width.

## Case III - Radiating Element and Slit of Comparable Dimensions

The source of radiation and slit size has comparable dimensions. The intense arc sources have dimensions from 0.25 x 0.25 mm, to 3.0 x 2.6 mm. Fluorescing regions caused by focused beams from incoherent (i.e. non-laser) radiation also have mm dimensions.

The two rules for most efficient coupling:

- Always fill the monochromator acceptance cone.
- Get as much light as possible through the slit while observing Rule 1.

Two lens systems, such as the one in Figure 5, simplify the design implementation because you can set the length of the collimated arm to suit your set up. You also need to use a large diameter optic for efficient collection from the source. Oriel Instruments’ Monochromator Illuminators exemplify efficient implementation of a single optic solution.

## Rule 1

Filling the acceptance cone means focusing the beam on the slit at the correct F/number. Focusing at these F/#s results in an overfill of the grating along vertical and horizontal diameters and underfill of the corners. If you focus at lower F/#, light is lost as it misses the grating and reflects inside the monochromator as stray light.

## Rule 2

Figure 5 shows a typical optical system. Light from a filament is collected by Lens 1, and focused on the monochromator slit by Lens 2. The magnification, m, of the filament on the slit is given by the ratio of the F/numbers.

m = (F_{2}/#)/(F_{1}/#)

Because the beam is "collimated", the beam diameter is approximately constant, so the magnification is also given by the ratio of the focal lengths, f_{2}/f_{1}.

**Figure 5. **A condenser and secondary focusing lens system.

## Condenser Lens

A simple model based on Figure 5 is very useful in showing the importance of choosing a low F/# lens for Lens 1 and in illustrating proper orientation of the source.

A uniform rectangular radiating element of dimensions "w x h" is assumed. Lens 2 is fixed. To allow for magnification, the F/# of Lens 1 must be (F/#_{2})/m, where "m" is the magnification of the radiating element to the slit. The effective slit dimensions are "a x b". When the source image completely overfills the slit, V is the ratio of slit area to magnified source area.

V = (a x b)/(mw x mh)

The power entering the slit is proportional to

The first term reflects how light collection is proportional to 1/(F/#_{1} )^{2}. The second term is the vignetting loss.

Figure 6. shows a typical graph of relative power through the slit vs. magnification. There are three regions. At very low magnification, V = 1, but very little power is collected. Power collected increases as m^{2}, and power into the monochromator obeys the same relationship.

At magnification m_{1}, the width of the radiating element image reaches the slit width, and V starts to decrease as 1/m. In this region

V* = a/mw

Therefore, the power relationship above allows for collected radiation to increase as m.

**Figure 6. **Relative power into the slit from a uniform rectangular source as the magnification of source onto the slit changes. The graphic above shows the three different regions of m.

## 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 leading instruments, such as light sources covering a broad range from UV to IR, pulsed or continuous, and low to high power.

Oriel also offers monochromators and spectrographs as well as flexible FT-IR spectrometers, which make it easy for users across many industries to build instruments for specific applications. Oriel is also a leader in the area of Photovoltaics with its offering of solar simulators that allow you to simulate hours of solar radiation in 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.