Our main aim was to configure a 4 Lens Relay System in order to observe the
MOT.
A diagrammatic representation of a 4 Lens Relay System is presented below.The first lens that could be used
in the system is either a
one inch or 1.5 inch doublet,this aperture being constrained by the system we are looking at, while the
remaining three lenses are two inch ones.The intent of using doublets instead of singlets was to enhance the image quality by reducing optical aberrations.We have further used the OSLO
Light software to study the Relay System using both singlets and doublets and tried to compare the efficiency
of both systems.
Our primary job was to setup the Relay System and experimentally quantify atleast three properties pertaining to
the system:
(a)Resolution and Magnification
(b)Transmission.
Resolution and Magnification were measured by imaging a standard catalogue(from Kodak) with our imaging
system.Transmission was measured by using a LED as the source.
The Resolution and Magnification of the Relay System was measured from a single experiment.The experimental setup looked similar to the picture alongside.When looking at 6.3 cycles/mm from the catalogue,where each cycle refers to a white plus a black line,our imaging system reproduced 6.3 cycles/mm.Similar results were reproduced when using 9 cycles/mm from the catalogue.Hence, we can very well conclude that we were able to produce a one to one imaging system.Also,even at 18 cycles/mm from the catalogue,we were able to quite clearly distinguish the adjacent black and white lines.As a result,we can conclude to certain level of arbitrariness that we can resolve to around 25 microns or below with our imaging system.Here,I would also like to add that the resolution of our CCD is 7.4 microns/pixel.
For this part we used a LED as our source.Since the focal length of the lenses we were using was 100mm,
we first placed the CCD camera at a distance of 100mm from the LED.
When using just the LED,the intensity profile on the CCD camera was pretty uniform as expected.Hence,we measured the total intensity incident in an area
A=109*175 sq.pixel of the CCD.The choice of this particular value of area was quite arbitrary.The intensity(in arbitrary units) measured
in this case was
I_in=2.77E05
Hence,I_in/A = 2.652E07 per cm^2
We then inserted the imaging system in between the LED and and the camera.The intensity profile on the CCD,as
expected for converging rays,was not uniform.Hence,this time we measured the total intensity incident(I_out)
on the CCD.
I_out=6.5E07.
Since we are using a one inch lens in the beginning of the system,we can compute the output intensity per square
cm in this case by just diving I_out by the area of the first lens,A'=5.06 cm^2.
Hence,I_out/A' = 1.283E07 per cm^2
So,our imaging system transmits around 48% of incident light.A photograph of the experimental setup
used in this case is shown alongside on the left.In this present setup,we have used two disconnected lens mounts with a mirror
in between.We were constrained to use this geometry in order to be able to fit the imaging system below the MOT.
As a result,inevitably,there is some misalignment in the system.This should be a good explanation for reduced
transmission,since we were looking for much better result as predicted by Oslo.Also, when we used this system to
observe the MOT(which replaces the LED),we obtained an image with significant amount of coma.
The image quality and transmission was quite improved using a rectangular connecter(as shown in the figures on right)which improved the alignment to a considerable extent.We can give a possible explanation of reduced coma in this case.Considering the first system,when the optic axis of the horizontal lens mount is not in proper alignment,then the rays reflected from the mirror,instead of appearing to come from an on axis point,would instead appear to come from an off axis point.Thus,we will be dealing with an oblique ray bundle and an off axis image point.As a result,this should contribute to increased amount of coma. In the next case,with proper alignment,we were able to reduce coma considerably and also improved on transmission.However,we are still having some residual coma,but I am not sure whether this is due to an alignment problem or something inherent with the lenses that we used.For those who are interested to know more about aberrations(which will also form a part of our later discussions),you can have a look at the Oslo Reference Manual. The image on the right shows our imaging system after it was placed under the MOT.
Here is a sample picture(on the left) that we obtained from our imaging system.For comarision,I have also
incorporated an image of the same MOT as observed by use of a commercial lens(right).As can be seen,the image
from our imaging system has a comet like aberration which is reminiscent of comatic aberration.This aberration
is not that prominent in the image taken by the commercial lens.However,the configured imaging system gives a
lot more freedom of utility which more than compensates for this not so huge aberration.The reasons for using
a self configured imaging system rather than a commercial one is discussed in some length later.
In our next part,we have analyzed the Imaging systems by using the software
Oslo Light.This part of our work can be
broken down into two important parts:
(a) study of transmission
(b) study of (monochromatic)aberrations.
We performed comparative studies for the following systems:
(System#1) Doublets:First lens-1 inch doublet,remaining lenses-2 inch doublets.
(System#2) Doublets:First lens-1.5 inch doublet,remaining lenses-2 inch doublets.
(System#3) Singlets:First lens-1 inch singlet,remaining lenses-2 inch singlets.
I will present the analysis of System#1 in some detail.The others follow in the same line.
As noted earlier,the lenses that we have used for this system are one 1 inch doublet and three 2 inch lenses.For those who are unfamiliar wih the Oslo Light. software,I would like to add that we can directly enter these lens specifications in the software and prepare what you may call a ray diagram for the system,from which we can calculate important quantities,and the quantities that we are interested in for this case,as I have stated earlier,is the transmission and aberration of the system.It boils down to entering the specifications of all the surfaces correctly.However,note that since we are using more than 12 surfaces here,we are constrained to use the licensed version of the software,whearas the above link leads you to the free version which works only for less than 10 surfaces.
After we are done with entering the lenses,we can cross-check whether the system is correctly entered by checking
the focal length of the entire system.This should be close to 100mm in our case.Once we are sure that we have
reproduced a correct representation of our system,we can directly proceed to calculate the transmission for this
system.This entails using a Lambertian source
and passing around 1E07 rays through the system and count the rays that make it through the system.The ratio
should give us the transmission percentage.We can then compare this value to what we would expect by pure
geometrical considerations,i.e,in a purely ideal situation where all the lenses are lossless.
Expected transmission from geometry considerations:
In this case,we will calculate the percentage of total light that is incident on the first lens from a Lambertian
source placed 100mm away.In an ideal case,all this light should be transmitted through the system.
Assuming that the lens is quite far away from the source,we can use a spherical geometry here.Since for a Lambertian
source,the radiance (power per unit solid angle per unit projected source area),L, is a constant,we can show with
some amount of calculation that the fractional energy striking the surface is just sin^2(A),where "A" is the angle
subtended by the lens to the source.This approximates to (l/d)^2.
Thus,when using the 1 inch lens,the fractional Intensity transmitted through the lens
T=(12.7/100)^2=1.61%.
Transmission as obtained from Oslo
In Oslo,we have traced 1E07 rays from a Lambertian source through our imaging system,having a wavelength of 0.78
microns.The limiting half angle for the Lambertian source is 90 degrees,i.e,the lambertian emits in an hemisphere.
I have used the dimensions of the Lambertian source to be a circle of 0.4mm radius.The details are attached
alongside(please click on the picture).The software gives us a result of 1.524% transmission,which is pretty
close to what we would expect ideally.
Aberration as obtained from Oslo
I have analyzed the siedel aberrations for the system.Oslo produces a file for the third order siedel aberration
coefficients.
SEIDEL ABERRATIONS:
| SA3 | CMA3 | AST3 | PTZ3 | DIS3 |
| 1.103337 | 0.000618 | 3.4654e-07 | 1.3387e-11 | 1.9425e-10 |
As noted earlier,the lenses that we have used for this system are one
1.5 inch doublet and three 2 inch lenses.
The expected transmission for this system from geometrical consideration is 2.3%.The value obtained from running
Oslo is 2.201%.
The Siedel aberrations are listed below:
| SA3 | CMA3 | AST3 | PTZ3 | DIS3 |
| 0.970849 | 0.001370 | 1.9327e-06 | 1.2509e-11 | 2.7270e-09 |
The lenses that we have used for this system are one
1 inch singlet
and three 2 inch singlets.The expected
transmission is 1.61% and Oslo suggests that it is 1.536%.
The aberration coefficients are listed below:
| SA3 | CMA3 | AST3 | PTZ3 | DIS3 |
| 1.764404 | -0.001180 | 7.8928e-07 | 1.3097e-11 | -5.2799e-10 |
We can already see that as far as quality of transmission is concerned,the systems are quite close to ideal.
If we could align the lenses and mounts properly,we should expect to get very good transmission irrespective
of which system we are using.However,the percentage of incident light transmitted depends on the system,which
may limit us to using a particular system.
The other important feature which differentiates between them are the aberration terms.
The salient features are:
(1) The most important aberration terms are due to spherical and comatic aberrations.
(2) System#1 and System#2 have quite similar spherical aberrations,however,the comatic aberration for System#2 is
almost twice that of System#1.However,System#2 collects about 44% more light than system#1,which will inevitably
give more intense image of the MOT.Hence,if we are in view of collecting more light,we have to opt for
System#2.However,if that does not constrain us,we may as well settle for System#1.
In our present setup,we have used the 1 inch lens for the first lens(System#1).However,we are contemplating on
using System#2,with the 1.5 inch lens in future,in order to collect more light.Knowing that this may lead to
increased amount of coma,we have
actually placed an order for a custom built 1.5 inch lens for the particular wavelength we are looking at.
Hopefully that will give better results.
(3) System#3 has significantly more spherical aberration,60% more than System#1.Since it collects the same amount
of light as System#1,there could be no proper reason to use it for the imaging system.
Althoug this may look somewhat off-topic,even then,I would like to discuss as to why we were interested in
building our own system rather than use a commercial one.
The important points are listed below:
(1) We have a much better signal to background/noise ratio for our imaging system.With the commercial one,the
signal to background ratio is atmost 3:1,but now we could easily reach 100:1 or better.
(2) We have more freedom on the endside of the imaging system.Right now,we could split the light into two
paths,which means that we do not have to replace the CCD and PMT back and forth,which in turn reduces systematic
error.In future,this would also help us if we are interested in polarization selection.
(3) The commerical lens has a certain working range. We want to put the first lens as close to the window as
possible, in this way, we can collect more light. So after we change to the reentrant window, the shortest
distance between lens and MOT should be around 10cm, this is already on the edge of the working range of the
commreical lens. Another thing is that the commerical lens will not not fit into the reentrant window either.
(4) People prefer to use the imaging system built by themselves, because they know what is going on better.