While lenses are used in the examples that follow, front surface concave mirrors coated for the spectral region of choice are preferred. A coating such as aluminium is highly reflective from 170 nm to the near IR whereas crown and flint glasses start losing transmission efficiency rapidly below 400 nm. "Achromatic Doublets" are routinely cemented with UV absorbing resins and their antireflective coatings often discriminate against the UV below 425 nm (this is due to the fact that such lenses are often used in cameras where photographic film may be very UV sensitive).
If lenses must be used in the blue to UV, then choose uncoated quartz singlets or air spaced doublets.
Figure 22. Typical Monochromator System
AS aperture stop
L1 lens 1
M1 mirror 1
M2 mirror 2
G1 grating 1
p object distance
from lens L1
q image distance
from lens L1
F focal length
of lens L1
d the clear aperture
of the lens (L1 in diagram)
The above diagram shows a typical monochromator system with
one fixed exit slit and one detector, however, all that
follows is equally applicable to a spectrograph.
6.1.1 Review
of Basic Equations
Thin lens equation:
(3-16)
Magnification (m):
(2-14)
For simplicity the diameter of an optic or that of its aperture
stop (AS) (assuming it is very close to the optic itself)
is used to determine the f/value. In which case Equations
(2-4) and (2-5) simplify to:
f/valuein =
p/d object
f/value (6-1)
f/valueout =
q/d image
f/value (6-2)
6.2 Establishing
the Optical Axis of the Monochromator System
6.2.1 Materials
-
HeNe laser
-
Lenses, mirrors, and other optical components as required for optimization (see Section 3)
-
Three pinhole apertures of fixed height above the table
-
Precision positioning supports for above
-
Optical bench, rail, or jig plate
6.2.2 Procedure
Assemble the above components so that the laser beam acts
as the optical axis which passes first through two pinhole
apertures, followed by the monochromator, and finally through
the third pinhole aperture.
The external optics and source will eventually be placed
on the optical axis defined by the pinhole apertures and
laser beam. Position the pinhole apertures so that the lenses,
etc. may be added without disturbing them.
Note: Reverse illumination may sometimes
be preferred where the laser passes first through the exit
slit and proceeds through all the optics until it illuminates
the light source itself.
Alignment of the components is an iterative process. The
goal is for the laser beam to pass through each slit center
and to strike the center of each optical element. The following
steps achieve this:
-
If a monochromator has a sine drive, then set the monochromator to zero order.
-
Aim the laser beam through the center of the entrance slit.
-
Center the beam on the first optic.
-
Center the beam on the next optic, and so on until it passes through the center of the exit slit.
-
If the laser does not strike the center of the optic following the grating, then rotate the grating until it does. Many spectrometers are not accurately calibrated at zero order, therefore, some offset is to be expected.
6.3 Illuminating
a Spectrometer
If a light source such as a sample or a calibration lamp
is to be focused into the entrance slit of a spectrometer,
then:
Ensure that the first active optic is homogeneously illuminated
(plane mirrors are passive).
Place a white screen between the entrance slit and the
first active optic (in a CZ monochromator, the collimating
mirror and in an aberrationcorrected
concave grating, the grating itself).
Check for "images", if
there is a uniform homogeneously illuminated area, all
is well.
If not, adjust the entrance optics until there is.
6.4 Entrance
Optics Examples
The majority of commercial spectrometers operate between
f/3 and f/15, but the diagrams that follow use drawings
consistent with f/3 and all the calculations assume f/6.
In the examples which follow, the lens (L1) used is a single
thin lens of 100 mm focal length (for an object at infinity)
and 60 mm in diameter.
The f/valueout of
the entrance optics must be equal to the f/valuein of the monochromator.
If necessary, an aperture stop should be used to adjust
the diameter of the entrance optics.
Remember when calculating the diameter of aperture stops,
to slightly underfill the spectrometer optics to prevent
stray reflections inside the spectrometer housing.
6.4.1 Aperture
Matching a Small Source
Example 1 (Figure 23)
The emitting source is smaller in width than the width
of the entrance slit for a required bandpass.
Figure 23. Small Source Case
1. Calculate the entrance slit width for appropriate bandpass (Equation 3-9). For this example, let the slitwidth be 0.25 mm.
Example Object: a fiber of 0.05 mm core diameter and
NA of 0.25.
Object emits light at f/2 (NA = 0.25). Spectrometer =
f/6.
2. Projected image size of fiber that would be accommodated by the system (given by entrance slit width) = 0.25 mm.
m = image size/object size = 0.25/0.05 = 5.0.
Therefore, q/p = 5, q = 5p.
Substituting into the lens Equation 3-16 gives p = 120 mm, and q = 600 mm.
To calculate d, light must be collected at f/2 and be projected at f/6 to perfectly fill the grating.
Therefore, p/d = 2, d = 120/2 = 60 mm.
Therefore, aperture stop = full diameter of L1.
Projection f/value = 600/60 = 10.
In other words, the grating of the monochromator, even though receiving light collected at f/2, is underfilled by the projected cone at f/10. All the light that could have been collected has been collected and no further improvement is possible.
Example 2
If, however, the fiber emitted light at f/1, light collection could be further improved by using a lens in the same configuration, but 120 mm in diameter. This would, however, produce an output f/value of
600/120 = f/5
Because this exceeds the f/6 of the spectrometer, maximum system light collection would be produced by a lens with diameter
d = q/(f/value) = 600/6 = 100 mm
thereby matching the light collection etendue to the limiting etendue of the spectrometer.
The collection f/value is, therefore,
f/valuein = p/d = 120/100 = 1.2
Since etendue is proportional to the square of the (f/value)-1, about 70% of the available emitted light would be collected at f/1.2 (see Section 3).
If the user had simply placed the fiber at the entrance slit with no entrance optics, only 3% of the available light would have been collected (light in this case was collected at the spectrometer's f/6 rather than the f/1.2 with etendue matching entrance optics).
6.4.2 Aperture Matching an Extended Source
Figure 24. Extended Souce Case
The object width
is equal to or greater than the entrance slit width (see
Figure 24).
The f/valueout of
the entrance optics must be equal to the f/valuein
of the monochromator. The object distance should be equal
to the image distance (absolute magnification, m, equals
1).
Aperture stops should be used to match etendue of the entrance
optics to the monochromator. Because the object is larger
than the slit width,
it is the monochromator etendue that will limit light
collection.
In this case, image 1:1 at unit magnification.
1. Taking lens L1
So for F = 100 mm, p = 200 mm, q = 200 mm (2F).
2. f/value of the monochromator = q/d = p/d = 6.
Then
d = q/(f/value) = 200/6 = 33.3
Therefore, aperture stop = 33.33 mm to fill the diffraction grating perfectly.
6.4.3 Demagnifying
a Source
In this case the f/value of the source is numerically larger
than that of the spectrometer. This is often seen with
a
telescope which may project at f/30 but is to be monitored
by a spectrometer at f/6. In this case etendue matching
is achieved by the demagnification of the source (see
Figure 25).
Figure 25. Demagnified Source Case
1. Calculate the entrance slitwidth for the appropriate bandpass(Equation (2-21)). Take, for example, 1.0 mm = final image size = entrance slit width.
2. Image projected by telescope = 5 mm and forms the object for the spectrometer.m = 1/5 = 0.2,
then from Equation (3-16). Taking lens L1 with F = 100 mm (given),
p = 600 mm, q = 120 mm.
Calculate d knowing the monochromator f/value = 6.
q/d = 6, d = 120/6 = 20 mm.
The aperture stop will be 20 mm diameter.
Light is gathered at either the aperture of the projected
image or 600/20 = f/30, whichever is numerically
greater.
6.5 Use of
Field Lenses
The concepts given in this section have not included
the use of field lenses. Extended sources often require
each pupil in the train to be imaged onto the next
pupil downstream
to prevent light loss due to overfilling the optics, vignetting
(see
Section 2.8).
-
Used when entrance slit height is large and the light source is extended.
-
A field lens images one pupil onto another. In Figure 26, AS is imaged onto G1.
Field lenses ensure that for an extended source and finite
slit height, all light reaches the grating without vignetting.
In Figures 26 and 27 the height of the slit is in the plane
of the paper.
Figure 26. Example of Field Lens Imaging One Pupil onto Another
Figure 27. Example of Illumination System with Field Lens
6.6 Pinhole
Camera Effect
When entrance optics are absent, it is possible for the
entrance slit to project an image of just about everything
before the slit into the spectrometer. This may include
the lamp, the sample, rims of lenses, even distant windows.
Section 3 describes how to correctly
illuminate a spectrometer for highest throughput. Following
this procedure will eliminate the pinhole camera effect.
Multiple imaging may severely degrade exit image quality
and throughput. On the other hand, the pinhole camera effect
is very useful in the VUV when refractive lenses are not
available and mirrors would be inefficient.
6.7 Spatial
Filters
Aperture and field stops may be used to reduce or even
eliminate structure in a light source, and block the unwanted
portions
of the light (e.g., the cladding around an optical fiber).
In this capacity, aperture stops are called spatial filters
(see Figure 28).
The light source image is focused onto the plane of the spatial filter. which then becomes the light source for the system.
Figure 28. Spatial Filter Case
