Lasers and lenses - University of Toronto

Lasers and lenses:
Choosing a laser for optical trapping, and
designing and constructing lens systems for
imaging.
Ryan McKenzie
August 25, 2004
University of Toronto
Department of Physics
Supervisor: Professor Joseph Thywissen
Table of Contents
1 Optical Dipole Trap
1.1 Theory…………………………………………. 2
1.2 Choice of Laser………………………………… 5
1.3 Lens Recommendations……………………….. 7
2 Imaging Systems
2.1 Overview and Construction……………………. 8
2.2 Resolution……………………………………… 10
Appendix 1: Contact Information……………………. 12
Appendix 2: OSLO
2.1 Installing OSLO………………………………… 13
2.2 Getting Started…………………………………. 13
2.3 Useful Features………………………………… 14
References……………………………………………. 15
1
Optical Dipole Trap
Theory
In the last 15 years, there has been a flurry of new developments in the field of
cooling and trapping neutral atoms, which has included ground breaking work leading to
two Nobel prizes. Steven Chu, Claude Cohen-Tannoudji and William D. Phillips were
awarded the prize in 1997 for the development of methods to cool and trap atoms with
laser light, and Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman were awarded the
prize in 2001 for the achievement of Bose-Einstein condensation using optical and
magnetic techniques.
An optical dipole trap (ODT) is a purely optical means of trapping neutral atoms.
A laser beam can be focused down to a point creating a radiation field with a maximum
in space [1]. The radiation field will induce a dipole in a neutral atom causing it to
become trapped. The trapping potential is dependant on detuning of the laser light from
the transition frequencies (frequencies of light emitted when an electron makes a
transition from one state to another) of the atom in question. Many alkali atoms have
transition frequencies in the visible or near infrared portion of the spectrum making them
ideal candidates for optical dipole trapping. An advantage of an ODT is that it is
independent of the magnetic properties of the alkali atoms being trapped.
An atom in an electric field E has a polarization p given by
p = áE ,
(1)
and the dipole potential U dip of a polarized atom in an electric field is given by
U dip = !
1
pE ,
2
(2)
where angle brackets indicate an average in time. Taken together this implies that the
dipole potential of an atom in an ODT is proportional to the electric field squared, and
therefore to the intensity of the incident laser beam. Power Pabs will be absorbed by the
atom and re-emitted as dipole radiation. The rate at which photons are emitted !sc , or the
scattering rate, is
"sc =
p& E
Pabs
=
,
h!
h!
(3)
where " is the frequency of the incident laser light and the emitted photon. This is once
again going to be proportional to the intensity of the laser beam. In [2], the atom is
!
2
treated as a simple two state oscillator, and the dipole potential and the scattering rate are
worked out to be
3"c 2 $
I , (4)
2# 03 %
2
3#c 2 & " )
"sc =
( + I , (5)
2h$ 03 ' % *
U dip =
!
where " 0 is the transition frequency, " = # $ # 0 is the difference between the laser
frequency and the transition frequency, and " is the damping rate due to radiative energy
!
loss (a constant). The above
equations make use of the “rotating wave approximation” in
which we assume " << # 0 and " " 0 # 1.
!
!
!
An important feature of the above equation for the dipole potential is that if the
laser is red detuned from the atomic resonance the potential is negative and the atoms
! light field; if the laser is blue detuned the atoms will be repulsed
!
will be attracted
into the
by the light field. Blue detuned traps are advantageous because the atoms are stored in a
“dark” place, which leads to lower scattering rates. This becomes a substantial advantage
for traps with hard repulsive walls (ex. a box) or deep traps for tight confinement [2].
This report will be concerned with red detuned traps as they are more cost effective and
easier to make. A red detuned trap is easier to make since it consists of a single focused
beam, whereas several beams are required to form the walls of a blue detuned trap.
Real atoms do not behave as two state oscillators, they have a complicated
substructure that leads to multiple transition frequencies. The most important transition
frequencies for our purposes will be the D line doublet, which arises due to the effects of
spin orbit coupling. Taking this effect into consideration the dipole potential and the
scattering rate become
"c 2# & 2
1 )
(
+I , (6)
U dip =
+
2$ 03 (' % D2 % D1 +*
#c 2" 2 & 2
1 )
(
+I , (7)
"sc =
+
2h$ 03 (' % D2 2 % D1 2 +*
where " D2
!
and " D1 represent the D2 and D1 frequency transitions respectively.
!
In the case of interest, 40K, the transition frequencies are # D1 = 2" ! 2446.0THz
D2 = 2" ! 2456.9THz , and the laser used in the trap will have a wavelength of
! and #!
1064nm, which corresponds to a frequency of # = 2" ! 1770.4THz . This gives a ratio of
" " D1,2 < 0.73 , meaning that the rotating wave approximation is not valid in this instance.
For this reason, in all subsequent calculations of trap potentials and scattering rates, I
have used the equations
!
3
U dip = "
3#c 2 & %
% )
+
+I ,
3 (
2$ 0 ' $ 0 " $ $ 0 + $ *
(8)
3
2
3#c 2 % $ ( % "
" (
"sc =
+
' *'
* I,
2h$ 03 & $ 0 ) & $ 0 + $ $ 0 + $ )
(9)
!
which are what you get by assuming that the atom is a two state oscillator before
invoking the rotating wave approximation. The " 0 used in this equation will be the
average of "!D1 and " D2 , this is better than the rotating wave approximation since
" D1 " D2 = 0.996 . The equations above give the following relationship between the
scattering rate and the dipole potential,!
!
!
!
3
1% $ ( % "
" (
"sc = # ' * '
+
* U dip .
h &$0 ) &$0 # $ $0 + $ )
(10)
In a 3D harmonic trap, where the trap depth is much greater than the thermal energy of
the atoms, kBT, the heating rate due to photon scattering is given by [2]
!
% $ (3% "
1
1
" (
˙
T = Trec"sc = # Trec ' * '
+
*U dip ,
3
3h & $ 0 ) & $ 0 # $ $ 0 + $ )
(11)
where Trec is the temperature associated with the kinetic energy gain by emission of a
single photon.
!
The intensity distribution of a focused Gaussian beam IFB propagating in the z
direction is given by [2]
IFB ( r,z) =
%
2P
r2 (
exp
$2
'
*,
2
"# 2 ( z)
& # ( z) )
(12)
where P is the power of the beam and " ( z) is the 1 e 2 radius of the beam (it is important
not to confuse this " with either the laser frequency or the transition frequency),
!
2
!" z = " ! 1+ # z & .
( ) BW
% (
$ zR '
!
(13)
2
The minimum radius of the beam " BW is known as the beam waist, and zR = "# BW
/ $ is
ˆ
the Rayleigh length !
of the beam. In order to calculate the maximum trap depth U and
heating rate for a beam, we calculate U dip (equation 8) at I(r=0,z=0),
!
!
!
!
4
6"c 2 $ & 1
1 ) P
Uˆ = 3
+
(
+ 2
# 0 2" ' # 0 % # # 0 + # * # BW
!
2*
( &) #
$ !
T& =
Trec
3h
2* $% ) 0 !"
3
& 1
1 #ˆ
$$
!!U .
+
% )0 ' ) )0 + ) "
(14)
(15)
The final quantity of interest is the Fermi temperature TF, which, in a 3D
harmonic trap, is given by [1]
(6N) 3 h(" r2" z )
1
TF =
kB
1
3
,
(16)
where N is the atom number and ! r, z are the oscillation frequencies of atoms in the trap
in the axial and radial
! directions. These frequencies are given by [2]
4Uˆ
, (17)
2
m" BW
2Uˆ
, (18)
"z =
mzR2
"r =
!
where m is the mass of the atom in the trap.
Choice of Laser
!
When choosing a laser for an ODT two important specifications to consider are
the pointing stability and the intensity stability of the laser. Poor pointing stability or
intensity stability will lead to heating in an ODT [3] [4]. A laser with a narrow frequency
range is also desirable. In a focused beam trap, frequency range is not a serious issue, but
if the laser is later used to make an optical lattice, a narrow frequency range then
becomes necessary. Pointing stabilities are generally measured in micro-radians over
some time interval (anywhere from a few seconds to several hours). The linewidth of a
laser is the width of the laser beam frequency. A laser’s intensity noise is generally
measured in two different ways: the first is the rms intensity noise given over some time
scale, typically 10Hz to 1Mhz, the second is the relative intensity noise (RIN), which is
the ratio of the mean square intensity fluctuation spectral density of the optical signal to
the average optical power squared measured in units of dB/Hz [5].
Another consideration to take into account when choosing a laser for an ODT is
the available power. The laser should be powerful enough to create a trap whose depth is
at least ten times the Fermi energy of the trapped atoms. As can be seen in equation (11),
5
a laser far detuned from the transition frequency of an atom will lead to a trap with a
lower heating rate. The cost of using a farther detuned laser (longer wavelength) is that it
will require greater power to create a sufficiently deep trap. Lasers from six different
companies were compared in order to choose the best laser at the lowest cost. Contact
information for a representative from each company is included in appendix 1.
Coherent offers several lines of high stability lasers, red detuned from the
transition frequency of 40K, with sufficient power to create an ODT. For example, their
899-21 series ring lasers and their MBR110 series Ti:Sapphire lasers are both viable
options; however, at a cost of around $100 000USD they are too expensive to warrant
serious consideration. Toptica’s TA100 series tapered amplifiers were also considered.
These lasers provide sufficient output power at appropriate wavelengths, but at a cost of
around $30 000USD there were cheaper options with similar specifications. A master
laser is also required to feed into the TA further increasing the cost. New Focus’s TLB
series diode lasers are inexpensive (around $10 000USD), high stability lasers at
wavelengths greater than the transition frequency of 40K. Unfortunately, New Focus is
unable to produce their TLB lasers at powers sufficient for creating an ODT.
The Versadisk from ELS (Electronic Laser System) was another possibility. The
Versadisk is a high powered Yb:YAG laser capable of producing up to 100W of power at
1030nm. ELS claims the Versadisk has a linewidth of <5Mhz, and the measured pointing
stability is 1.1µrad over 30minutes. They also claim that the laser has a RIN of <150dB/Hz. These specifications match the specifications of all the other lasers
considered, however, other lab groups have had problems with ELS meeting their
advertised specifications in the past. The Versadisk is also an expensive laser, at 5W (the
lowest available power) it costs over $40 000USD. At 1030nm a laser with a tenth this
power is adequate. For these reasons, it was decided that the Versadisk is not the right
choice for an ODT.
The best lasers considered were from the Mephisto product line by InnoLight. At
1064nm a laser with at least 200mW would create a deep enough trap and at 1319nm
250mW would be sufficient. The Mephisto 500 and the Mephisto MIR 500 meet these
requirements respectively. These solid state lasers have an advertised linewidth of about
1kHz, and a pointing stability of 2.1µrad over 1hr 20min. The RIN of the Mephisto
lasers is about –100db/Hz, or –150dB/Hz with the noise eater option. Unfortunately, the
Mephisto product line is expensive, the Mephisto 500 costs $25 900USD and the
Mephisto MIR 500 costs $48 000USD.
The laser that was purchased was a 1064nm solid state (Nd:YAG & Nd:YVO4)
laser from CrystaLaser. The rms intensity noise for the CrystaLaser is <0.1% if the
ultralow noise version is purchased, which matches the rms intensity noise specification
of the Mephisto. The advertised linewidth and pointing stability of this laser are <10kHz
and 5µrad respectively, which are worse than the Mephisto in both cases. However, at
500mW the ultrastable version of the CrystaLaser is available for about $10 000USD,
making it the most cost effective choice.
6
!
The table below shows theoretical trap depths, heating rates and the Fermi
temperature for a 1064nm laser. All calculations were made assuming an atom number
of N = 10 6 and a beam waist of " BW = 20µm . The recoil temperature Trec and Γ were
taken from [2]. The transverse ! r and longitudinal ! z oscillation frequencies may be
calculated from equations 17 and 18. For example at 200mW, " r = 9.57 ! 103 rad s and
" z = 1.15 ! 102 rad s . !
Table 1: ODT information for a 1064nm laser
Power (mW)
Trap Depth
Heating Rate
(µK)
(µK/s)
Fermi Temp
(µK)
Trap Depth/
Fermi Temp
10
2.2
0.002
0.68
3.2
30
6.6
0.006
1.2
5.5
60
13.2
0.01
1.7
7.8
100
22.0
0.02
2.1
10.5
200
44.0
0.04
3.0
14.7
500
110.1
0.1
4.8
22.9
Lens Recommendation
The first consideration when purchasing a lens for focusing the beam of the ODT
should be what focal length to use. The vacuum chamber is 7.5cm wide meaning that the
atom cloud to be trapped will be located approximately 3.75cm inside the cell. This
means that the focusing lens must have a focal length of 4cm or greater. There should be
space for this directly opposite the BEC imaging system. According to the rules of
Gaussian optics, in order to obtain the smallest spot size (focus of the laser) the largest
possible lens with the shortest possible focal length should be used [6]. However, due to
aberrations introduced by real lenses this is not always the case.
A good choice of lens for the ODT are the achromatic doublets available from
Thorlabs. These lenses do a much better job of limiting aberrations than a spherical
singlet and can be made much larger than an aspheric lens. The lens I would recommend
using is Thorlabs AC254-060-B, which has a diameter of 2.54cm and a focal length of
6cm. This choice was made by looking at the spot diagrams for Thorlabs near IR
achromatic doublets and picking out the lenses with an rms spot size less than 10µm. Out
of these lenses the lens with the smallest Airy disk was than selected despite the fact that
it may not have been listed as having the smallest rms spot size. This was done because
Thorlabs specification sheets show the minimum spot size for a combination of 706.5nm,
855nm and 1015nm light, whereas at any given wavelength the minimum spot size is
often diffraction limited. The 1064nm laser that was purchased is right on the boundary
between Thorlabs near IR and IR lens classes. It may be worthwhile to look at Thorlabs
IR lenses and see if any will perform better than the lenses in the near IR category.
7
Incidentally, both the Thorlabs specification sheets and the ray tracing program OSLO
often show lenses as having better than diffraction limited performance. This is because
the geometrical ray tracing algorithms they use do not take into account diffraction
effects.
The Thorlabs specification sheet lists the AC254-060-B as having an rms spot
radius of 8.688µm and an Airy diameter of 5.467µm using a 706.5nm, 855nm, 1015nm
light. The total length of the system (from the first lens surface to the focal point) is
listed as 63.36mm. The lens was recreated in OSLO using the data from the Thorlabs
catologue. At a distance of 63.35mm in front of the lens with the wavelengths specified
above, OSLO determined the rms spot radius to be 8.637µm and gave an Airy diameter
of 5.462µm, which leads me to believe that OSLO has made an accurate recreation of the
Thorlabs lens. Using OSLO, the rms spot radius at 1064nm of the lens was determined to
be 3.982µm, with an Airy radius of 3.405µm at a distance of 55.75mm in front of the
front surface of the lens. A beam radius of 11.43mm was used. This leads me to believe
that the lens is capable of producing spot sizes of around 4µm radius 5.6cm if front of the
lens.
Imaging Systems
Overview and Construction
In order to observe ultra-cold atoms in the vacuum cell, imaging systems are
required. The current set up makes use of four different imaging systems: one to observe
the cloud of atoms in the MOT, one to line the MOT cloud up over the chip, and two in
order to observe atoms magnetically trapped by the chip. Each imaging system makes
use of two lenses in order to form an image on the CCD of a Micropix M-640 camera. If
the first lens (through which light enters) has focal length f1 and the second has focal
length f 2 , then the magnification of the object will be M = f 2 f1 . Ideally, the object
should be located f1 in front of the first lens causing the image to be formed f 2 behind
the second lens; however, if the object is located slightly in front of or behind the focus of
!
the first lens the image will just be formed slightly in front of or behind the focus of the
! second lens. There are only two cameras available
!
for the four imaging systems. The
! is mounted permanently to the MOT imaging system. !
first camera
The second camera is
attached to four metal rods that can be used to mount it to any of the three remaining
imaging systems.
The MOT imaging system consists of an AC254-075-B (f=75mm) Thorlabs
achromat and an AC254-035-B (f=35mm) achromat. The system had already been built,
but the camera was mounted to a large translation table in order to adjust the focus. This
translation table was exchanged for a smaller focusing knob with a diameter slightly
larger than the diameter of the imaging lenses. In order to obtain the proper
magnification factor, and in turn an image with minimal distortions the lenses should be
set up a distance of f1 + f 2 apart. To accomplish this, a laser beam was shone into the
lens system and the distance between lenses was adjusted until the outgoing beam was
!
8
collimated. A ruler was then imaged in order to ensure that the system was magnifying
objects properly. In order to determine the actual size of an object imaged with the MOT
system, the image should be multiplied by a factor of 2.15 ± 0.02 . The theoretical
magnification given by this system is f 2 f 1 = 2.14 .
The first BEC imaging system consists
! of two AC254-075-B (f=75mm) Thorlabs
achromats. The distance between the lenses and the magnification of the system was
determined in the same manner as for the MOT imaging system. The magnification
factor for this system was found to be 1.000±0.006. The second BEC imaging system
consists of two AC254-100-B (f=100mm) Thorlabs achromats. This system was built
with a 90 degree bend in its middle so that it would fit in its allocated space. The
magnification factor for this system was calculated to be 1.004±0.004. Both these
magnification factors match the theoretical values of 1.0.
The chip alignment imaging system was built with left over parts from the other
three systems. The first lens is an f=15cm achromat and the second lens is an f=10cm
plano-convex lens. The imaging system has a 90 degree bend in it so that it may be
positioned under the vacuum chamber looking up at the magnetic chip trap. Figure 1 is
an image of the magnetic chip trap taken with the chip alignment imaging system.
Figure 1: The magnetic chip trap
9
Resolution
A standard for determining the resolution of an optical system is the Rayleigh
criterion, which states that two objects are just resolved when the bright central maximum
of the diffraction pattern from one object coincides with the first minimum of the
diffraction pattern from the second. For a thin slit, and for a circular aperture the
intensity distributions I (! ) are given by [6]
$ sin(# ) ' 2
I (" ) = I (0)&
),
% # (
(19)
$ 2J1 (# ) ' 2
(20)
I (" ) = I (0)&
)
% # (
respectively, where J!
1 indicates a first order Bessel function. An important fact that can
be determined from these distributions is that for two slits the resolution corresponds to
the distance between the slits when the central minimum intensity is 8 / " 2 the maximum
intensity, and for two!circular apertures the minimum is 0.736 the maximum intensity.
Another method of characterizing the resolution of an imaging system is with the
!
modulation transfer function (MTF). The modulation of an image is defined to be [6]
Modulation =
Imax " Imin
,
Imax + Imin
(21)
and the modulation transfer function is defined as the ratio of input modulation to output
modulation. For equally spaced lines, the Rayleigh criterion corresponds to an MTF of
! the background light intensity is subtracted so the input modulation
10.5%, provided that
is one.
A one micron pinhole was imaged with the straight BEC imaging system in order
to try to determine its resolution. Unfortunately, the data taken is not reliable because the
signal saturated. According to the Rayleigh criterion the resolution of the system should
be half the base of the intensity distribution due to the pinhole. The intensity distribution
of a pinhole given by (20) is difficult to fit to due to the Bessel function. However, the
distribution resembles a Gaussian so a Gaussian was fit to the data. This leaves some
ambiguity as to what exactly constitutes the base of the distribution. For this reason,
instead of calculating the base of the distribution, the width of the distribution was
calculated at 0.37 times the maximum intensity value (this width corresponds to half the
base of the distribution). If the intensity distribution is given by
10
$ "x 2 '
I(x) = I (0) exp& 2 ) ,
% 2# (
(22)
we are interested in finding the width when I ( x ) = 0.37I (0) . This corresponds to a width
of
!
(
)
l = 2x!= 2" 2ln 1 0.37 .
(23)
The average sigma value of the distribution obtained from the one micron pinhole was
" # 1pixel which gives a resolution of l = 2.8 pixels = 20.9µm .
!
!
A microscope slide with a grating spaced by 20µm was used to determine the
modulation of the imaging system (at 20µm). Since, according to the calculation above,
!
this should be near the resolution of the imaging system, the minimum value of the
intensity distribution should be 8 " 2 of the maximum value (after subtracting away the
background). As noted above, this corresponds to a modulation of 10.5%. In order to
determine the background intensity, a dark spot on the slide was imaged (a comparatively
large number written on the slide). This value was then subtracted from the average of
! of the grating to find the maximum intensity, and subtracted
several peaks of the image
from the average of several valleys to find the minimum intensity. This gave a
modulation of 36%. This discrepancy from the expected value of 10.5% indicates that
either the resolution determined from the pinhole is better than the value calculated
above, or the modulation determined from the grating is worse than 36%. It is my belief
that the saturated intensity measurement caused sigma to be larger than its actual value,
and that the resolution of the imaging system is better than 20µm.
Further work would include more careful comparison of modeling results and
measurements. Measurements could be improved with more careful attempts at imaing
the one micron pin hole, and by using a high resolution scanning-slit beam profiler to
eliminate camera-related problems.
11
Appendix 1
Contact Information
Laser Companies
1. Coherent-
Michael Boehlke
[email protected]
2. CrystaLaser
3. InnoLight-
Yvonne Chao
[email protected]
Tel: 800-334-5678 508-478-6200 x18
Fax: 508-478-5980
4. New Focus-
Min Chen
[email protected]
Tel: 408-919-5353
Cell: 408-516-8807
Fax: 408-516-8807
5. Toptica
Alain Bourdon
[email protected]
Tel: 413-562-5406
6. Electronic Laser System Corp. (ELS)
Patrick G. McNamara
[email protected]
[email protected]
Tel: 619-463-1925
Fax: 619-374-2756
OSLO
1. Lambda Research Corporation - Karen M Hoch
[email protected]
12
Appendix 2
OSLO
Installing OSLO
The ray tracing optics software OSLO is meant to be run on a Windows. In order
to run OSLO on a Macintosh a virtual PC must first be installed on the computer. The
virtual PC software is located in the Mac software case, and has already been installed on
the computer Antimony. In order to create a virtual PC on Antimony, simply open the
applications folder and select “virtual PC” from the list that pops up. The installation
instructions are simple and well documented in this folder.
Once you have a virtual PC, or if you are on a windows machine, you may install
OSLO. The CD containing OSLO is located in the PC software case, and the necessary
passwords and instructions are located inside the OSLO Optics Reference manual. In
case these papers are ever lost the access number is 523E2 BE179 95C19 A65A2 and the
installation password is maxwell63. Our current copy of OSLO is only licensed to run
until November, and will stop working at some point during that month.
Getting Started
As an introduction to using OSLO, I thought it would be easiest to run through the
step by step procedure for recreating a Thorlabs achromatic lens. Consider, for example,
the Thorlabs AC254-150-B, a 25.4mm diameter, 150mm focal length achromatic lens.
To start, open OSLO then go to “file” and choose “New Lens”. Choose “Custom lens”
from the possible options, give it a name and press “OK”. One of the windows that pops
up should be labeled “Surface Data”, this is the window into which you will enter all the
information about your lens. The achromatic lens will require 3 surfaces, and a fourth
surface must be used as an image stop. In order to add a surface, just right click (ctrl +
mouse on the Mac) in the surface column and choose “insert before/after” from the menu
that pops up. Next enter all the necessary data from the Thorlabs catalogue in the
appropriate columns in the “Surface Data” window. This includes the radii of curvature
(r1, r2, r3), the thickness of each half of the lens ( t c1 and t c 2 ), the aperture radius or radius
of the lens (12.7mm in this case), and finally the type of glass used (in this case LAKN22
and SFL6). OSLO requires you to define an aperture stop for the lens, it is usually most
convenient to just use the first surface. If you now click on the button labeled “Draw
!
!
Off” your lens should appear.
If you want the range of the incident and outgoing light rays to be longer, select
“Lens” from the main toolbar, and then select “Lens Drawing Conditions”. You can
change “Initial/Final Distance” in order to show a greater distance in front of and behind
the lens. After you have changed the values just click on the green check mark twice and
the “Surface Data” window will reappear. If you want the entering beam to be wider,
you can change “Ent beam radius” in the “Surface Data” window. Thorlabs uses a
13
combination of three wavelengths when it calculates all of its specifications. In order to
change the wavelength used for calculations by OSLO, go to “Wavelengths” and enter
the desired values (in µm).
Useful Features
The following section contains the features in OSLO I found most useful. In
addition to the “Surface Data” window there is a window labeled “UW1”. Among other
things, this window contains a toolbar with buttons to show both a 2D and a 3D view of
the lens or optical system being investigated. Another useful feature is the group feature.
Highlight the surfaces you wish to group, right click on them and select “Element
Group”. These surfaces will then be treated as a unit, which is particularly useful if you
want to quickly turn around lenses.
OSLO can also be used to place an object in front of a lens or lens system. In the
“Surface Data” window go to the row labeled object and under thickness enter the
distance you want the object to be in front of your first lens. To adjust the height of the
object click on the “Setup” tab in the “Surface Data” window and enter whatever height
you wish. To adjust the number of rays emanating from an object, and the position on
the object from which they originate, click on “Lens” and go to “Lens Drawing
Conditions”. The columns at the bottom of the window that pops up allow you to adjust
these parameters.
Another useful feature of OSLO is the evaluate menu, which contains options for
creating spot diagrams and modulation transfer functions (MTF’s). The spot diagrams
and the MTF’s will be determined at the image stop of the system. In order to determine
a lens or a lens systems best characteristics these measurements should be made at the
minimum rms spot size of the system. To do this, in the row labeled IMS, click on the
box beside the thickness column and select “Autofocus – minimum rms spot size”. You
may then choose between the monochromatic minimum spot size (the minimum spot size
for the primary wavelength) and the polychromatic minimum spot size (the minimum
spot size for the combination of all three specified wavelengths). To view a spot
diagram, go to the “Evaluate” menu, choose “Spot Diagram” and then choose “Single
Spot Diagram”. I usually use all the default settings, except I change dots to symbols and
I usually like to show the Airy pattern in the plots. In order to view an MTF for a lens
system, choose “Spread Function” then “Through Frequency Report Graphic” from the
“Evaluate” menu. Enter the maximum number of lines per mm you wish to see the MTF
for and click OK. The features listed above by no means constitute an exhaustive list of
the possible applications of OSLO, they are just a small fraction of the things the program
is capable of.
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References
1. C.J. Pethick & H. Smith, Bose-Einstein Condensation in Dilute Gases
(Cambridge University Press, New York, NY, 2002).
2. Rudolf Grimm, MatthiasWeidemuller and Yurii B. Ovchinnikov, (2000) Adv. At.
Mol. Phys 42, 95.
3. T.A. Savard, K.M. O’Hara and J.E. Thomas, (1997) Physical Review A 56, 1095.
4. M.E. Gehm, K.M. O’Hara, T.A. Savard, and J.E. Thomas, (1998) Physical
Review A 58, 3914.
5. Relative Intensity Noise, Phase Noise, and Linewidth (2002)
http://www.agility.com/pdf/Relative_Intensity_Noise_Phase_Noise_and_
Linewidth.pdf
6. Eugene Hecht, Optics 4th Edition (Addison Wesley, San Francisco, CA, 2002)
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