Section 6: Entrance Optics
6.1
Choice of Entrance Optics
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 anti reflective 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.
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:
1/F = 1/p + 1/q (316)
Magnification (m):
 (214)
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 (24)
and (25)
simplify to:
f/valuein
p/d object f/value (61)
f/valueout
q/d image f/value (62)
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 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 aberration
corrected 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.
1) Calculate the entrance
slitwidth for appropriate bandpass (Equation (39)). For
this example, let the slitwidth be 0.25 mm.
2) Example Object: a fiber
of 0.05 mm core diameter and NA of 0.25.
3) Object emits light at
f/2 (NA = 0.25). Spectrometer = f/6.
4) Projected image size of
fiber that would be accommodated by the system (given by entrance
slitwidth) = 0.25 mm.
Calculate magnification to
fill entrance slit.
5) m = image size/object
size = 0.25/0.05 = 5.O.
Therefore, q/p = 5, q = 5p.
6) Substituting into the
lens Equation (316) gives p = 120 mm, and q = 600 mm.
7) 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/l, 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/q = 120/100 = 1.2
Since etendue is
proportional to the square of the (f/value)-l,
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
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 slitwidth, it is the monochromator etendue that
will limit light collection.
In this case, image 1:1 at
unit magnification.
l) 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.
3) Then
d f/value = 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.
1) Calculate the entrance
slitwidth for the appropriate bandpass(Equation (221)).
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 (316).
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 Fig. 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.
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.
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