Sodium Laser Guide Star Brightness, Spotsize, and Sodium Layer

So dium Laser Guide Star Brightness, Sp otsize, and So dium

Layer Abundance

a a a a a b

Jian Ge , B.D. Jacobsen ,J.R.P. Angel ,P.C. McGuire ,, T. Rob erts , B. McLeo d

a a,c

M. Lloyd-Hart , D. Sandler

Steward Observatory, The UniversityofArizona,Tucson, AZ 85721, USA

Center for Astrophysics, MS 20, 60 Garden Street, Cambridge, MA 02138, USA

ThermoTrex Corp oration, 10455 Paci c Center Court, San Diego, CA 92121, USA

ABSTRACT

We rep ort on new results of simultaneous measurements of so dium layer abundance and the absolute return ux

from laser guide stars created by a mono chromatic 1 W cw laser, tuned to the p eak of the so dium D2 hyp er ne

structure. The return was conducted at the MMT and the so dium abundance was measured at the CFA 60 inch

telescop e, ab out 1 km away from the MMT, with the Advanced Fib er Optic Echelle (AFOE) sp ectrograph. The

laser frequency stability,which can greatly a ect the return ux, was monitored at the same time in order to improve

the measurement accuracy. After the correction of laser frequency jitter and atmospheric transmission, the absolute

6 1 2

ux return for circularly p olarized lightis1.7110 photons s m per watt launched, p er unit column density,

9 2

whichwe take as our measured mean over the year of N(Na) = 3.710 cm at Tucson. The solidi cation of a

nal well-determined relationship b etween the so dium laser guide star brightness and so dium layer column density

is pivotal in the design of the next generation laser guide star adaptive optics systems.

We also rep ort the measurements and analysis of the relationship b etween the pro jected b eam waist of the so dium

laser and the resultant sp ot size on the so dium layer under typical atmospheric conditions. Knowledge of the waist

size is crucial to the design of the laser b eam pro jector for optimal p erformance. By pro jecting the laser through

di raction limited optics of roughly 3 r diameter, wehaveachieved the smallest arti cial b eacon yet recorded, ab out

0.8 arcsec.

Keywords: Adaptive Optics, Laser Guide Star, So dium Layer Abundance, Point Spread Function

1. INTRODUCTION

Adaptive optics (AO) systems can signi cantly reduce atmospheric distortion e ects in astronomical imaging if a

bright light source is available within arcmin eld-of-view of a scienti c ob ject for measuring wavefront phase errors.

However, the sky coverage for the AO systems relied on natural bright eld stars is only a few p ercentage of the sky

(e.g. Ro ddier 1995). In order to signi cantly increase the sky coverage with AO correction, laser-generated arti cial

guide stars or \b eacons" are required for sensing the wavefront errors (e.g. Sandler et al. 1994). The most promising

arti cial laser guide star is generated by fo cusing a so dium laser b eam tuned to the so dium D line at 589 nm on

the mesosphere so dium layer at ab out 90 km altitude.

Several groups in the world have b egun to explore the use of so dium laser guide star technique for astronomical

adaptive optics (e.g. Jacobsen et al. 1993; Max et al. 1994; Jelonek et al. 1994; Avicola et al. 1994). In

the Fall 1996, our group successfully closed the laser guide star adaptive optics tip-tilt system lo op resulting in

the rst rep orted improvements in image quality(Lloyd-Hart et al. 1997). In early 1997, Livermore laser guide

star group also successfully closed their high order AO lo op and made signi cant image corrections (Olivier et al.

1997). The recent closed lo op exp eriments with so dium laser guide stars at Max-Plank-Institut fur Astronomie have

also demonstrated a factor of two image improvements in the near-IR (Hippler et al. 1998). These exp eriments

demonstrate the p ossibility of so dium laser guide star technique in adaptive optics applications. However, there is

as yet no consensus on the optimum laser and p ower. The choice dep ends not only on the laser p ower, but also on

Other author information: (Send corresp ondence to Jian Ge)

J. G.: Email: [email protected]; WWW: http://qso.as.arizona.edu/ jge; Telephone: 520-621-6535;Fax: 520-621-1532

the inherently di erent pulse formats and frequency purity of di erent laser typ es. Theoretical calculations predict

di erences in return for the same p ower and column density up to a factor 5 according to pulse format (Milonni

&Telle, 1996, private communication), but these haveyet to b e con rmed exp erimentally.Thus, exp eriments that

measure column density and details of the excitation and scattering prop erties of so dium atoms in the so dium layer

are very imp ortant to re ne the design parameters of the laser and assess the p ower requirement.

Simultaneous lo cal observations of the so dium column density and the laser return are necessary to obtain the

fundamental relationship b etween the magnitude of the laser guide star and so dium abundance. Previous studies

have shown that the column density of the so dium layer varies with time, including long term seasonal variations

and short term variations (e.g. Pap en 1996; Ge et al. 1997), and also varies with latitude (Hunten 1966; Magie

et al. 1978; Pap en et al. 1996; Ge et al. 1997). A simultaneous measurementofcolumndensity and guide star

brightness has not b een done b efore. This together with the measurements of so dium layer abundance variation (Ge

et al. 1997) will provide a reference for the design of the so dium laser for the MMT 6.5 m AO system as well as

other so dium AO systems in the world.

In order to obtain the strongest signal from a so dium laser guide star for wavefront sensing and correcting, the

images at a Shack-Hartmann wavefront sensor should b e as sharp as p ossible. A doubling of the image would require

a quadrupling of laser p ower to obtain the same signal/noise ratio (e.g. Sandler et al. 1994). The instantaneous sp ot

size on the so dium layer is directly related to the so dium laser b eam waist size. The optimal so dium laser b eam waist

width varies with the instantaneous atmospheric conditions. Therefore, a series of exp eriments need to b e conducted

to nd out the relationship b etween the optimal so dium b eam waist and sp ot size and howtight a sp ot the laser

b eam pro jector generates on the sky.

In this pap er we will rep ort on simultaneous so dium laser return and mesosphere so dium abundance measure-

ments, instantaneous so dium b eam waist width and sp ot size measurements.

2. SIMULTANEOUS SODIUM LASER RETURN AND COLUMN DENSITY

MEASUREMENTS

The most prop er way to determine howmuch laser p ower is required for certain laser guide star AO p erformance is

to directly calibrate the laser p ower with the simultaneous measurements of so dium laser guide star ux and so dium

layer abundance. The continuous-wavedye laser we used for the MMT FASTRACIIAO system can provide a single

longitudinal mo de with tunable frequency at high p owers after it passes through a traveling-wave ring cavityand

frequency tuning elements (Rob erts et al. 1997). It is p erhaps the simplest laser for the simultaneous measurements.

The observational results can b e easily understo o d and provide a go o d reference for predicting other laser guide star

p erformance. Furthermore, the results provide a direct testing of current theoretical mo dels for so dium laser guide

stars (Milloni & Telle 1997, private communications).

The simultaneous measurements of so dium laser return ux and mesosphere so dium abundance were conducted

in March, May, and Septemb er, 1997. The so dium laser return ux was measured at the Multiple Mirror Telescop e

(MMT) on Mt. Hopkins. The laser output p ower was measured b efore and after each collecting data set with typical

10 image frames, whichwere typically taken in totally ab out 3 minutes. The exp osure time of each frame is 3-5

seconds. The average laser p ower pro jected on the sky is ab out 1 watts for the all three runs. Only the so dium return

ux during photometric conditions were used for the nal data analysis. In fact, during each return exp eriment the

laser b eacon images were used for cho osing those photometric measurements b ecause any thin clouds passing through

the laser b eams would showvery strong Rayleigh scattering and signi cantly reduce the return ux from the so dium

sp ot. Esp ecially during the Septemb er run, b ecause thin clouds covered part of the sky,we to ok advantage of the

laser b eacon high sensitivity to thin clouds to use the laser return images to help nd clear sky patch for the return

measurement.

The so dium layer abundance was measured at the CFA60inch telecop e with the Advanced Fib er Optic Echelle

(AFOE) sp ectrograph. The telescop e is only ab out 1 km away from the MMT on the same mountain. Therefore,

similar so dium layer patches were observed by b oth telescop es. The sp ecrograph resolving p ower is R = 50,000

(Brown et al. 1994). With such sp ectral resolution, the so dium D line is blended with telluric water absorption

lines, the D absorption line, which is clearly separated from other nearby telluric absorption lines, is therfore the

only suitable line for the so dium abundance measurements. Because the very weak telluric so dium D absorption line 1

Figure 1. Typical image frame of the so dium resonant uorescence recorded at the MMT with an Ap ogee CCD

camera for the simultaneous so dium laser return measurements. The dimension of the frame is 140x140 arcsec .

could b e easily buried in much stronger interstellar D absorption lines and/or stellar D absorption itself from late

1 1

typ e stars, only a couple of very nearbyearlytyp e stars without interstellar or stellar D absorption are suitable for

the measurements. Ab out a dozen of nearbybright early typ e stars with magnitude brighter than 3 magnitude have

b een searched by us to nd suitable targets for this pro ject. So far only four such stars were found, and they are

Leo, Aql, Tau and And. However, the numb er of stars suitable for the measurements will increase once higher

resolution sp ectra are obtained b ecause higher resolution will help to separate telluric D line from other interstellar

D lines (cf. Welty et al. 1994) and also stellar D line b ecomes much broader than the telluric D line.

1 1 1

Because the equivalent width of typical telluric so dium D absorption line is less than 1 mA, in order to measure

the so dium abundance to b etter than 15% error, a signal-to-noise ratio (S/N) of at least 1,000 is required for sp ectral

resolution R 50,000. With 16 bit CCD readout electronics, a S/N of 500 can b e reached in each frame. On

the other hand, once the S/N reaches ab out 500, CCD pixel-to-pixel variation will limit improvements in S/N. To

solve this problem, wecoadded 100 at frames, whichwere taken a few hours b efore or after the simultaneous

exp eriments for accurately tracing the CCD pixel sensitivityvariation, and divided the combined ob ject frames (

Leo in the March run, and Aql in the May run and the September run) by the combined at. The resulting S/N

can reach as high as 2,000, which is go o d enough for accurate so dium abundance measurements.

Figure 1 shows the typical image of the so dium resonant uorescence observed through one of the MMT mirror

during the Septemb er run. In order to avoid p ossible saturation of so dium laser p ower on the so dium layer, we let

the telescop e a little out of fo cus to the so dium layer. The average sp ot size for the all three observational runs is

ab out 3 arcsec, or ab out 1.3 m diameter on the so dium layer. We also p ointed the telescop e to the direction close

to the bright stars, whichwere chosen for measuring the telluric so dium abundance, to sample the similar so dium

layer patches.

The laser guide star and standard star images were recorded by a thermally co oled Ap ogee CCD camera mounted

on the telescop e. The data were reduced in the standard way with the IRAF package. The photometry of laser guide

stars and standard starswas measured by using the IRAF package PHOT. The estimated error of the photometry is 1.01

0.99

0.98

0.97

1.01

0.99

0.98

0.97

1.01

0.99

0.98

0.97

5888 5890 5892 5894 5896 5898

Figure 2. Typical telluric so dium D absorption sp ectra obtained at the CFA60inch telescop e with AFOE

sp ectrograph andR=50,000.The absorption lines from water vap or are much stronger for the Septemb er data

than those for the MarchandMay data.

2.5% based on the standard star ux measurements.

Figure 2 shows the typical telluric D absorption sp ectra from the September run, as well as from previous runs.

Telluric D lines from the three di erent runs show similar line strength. However, the absorption lines from telluric

water vap or are signi cantly di erent, esp ecially those water lines from the September run are much stronger than

those from the other two runs. The strong water absorption lines in the Septemb er data are almost blended with the

weak D line. Therefore, this gure further demonstrates that the sp ectral resolving p ower of 50,000 is a minimum

requirement for accurate measurements of so dium layer column density under di erentweather conditions.

Previous studies show that the mesosphere so dium D absorption is normally very weak, e.g. the typical optical

depth at the center of the absorption line is 0:04 << 1 (Ge et al. 1997; Ge, Angel & Livingston 1998), it is

appropriate to assume that the D absorption line, which line strength is a half of the D line (Morton 1991), is in

1 2

the linear p ortion of the curveofgrowth, where the column density of the atoms is prop ortional to the equivalent

width. The integrated numb er of so dium atoms p er square centimeter in the line of sight is then given by

2 20

cm ; (1) N =1:130 10

where W is the equivalent width, and b oth W and are in unit of A, f is the oscillator strength (f =0:318 for the

D transition at 5895.94 A Morton 1991). The error resulting from neglecting the saturation e ect was estimated to

b e less than ab out 2.5%, which is within the measurement error of ab out 10% caused by the photon statistics.

The measurement results from 1997 MarchandMay runs have b een published in the workshop pro ceeding on

Laser Technology and Laser Guide Star Adaptive Optics Astronomy (Ge et al. 1997). A strong correlation has b een

found b etween the absolute laser guide star ux and so dium layer abundance. Further, the circularly p olarized laser

b eam provides 30% increase in uorescent return over linearly p olarized b eam. The measurement errors from the

column density and the guide star brightness have b een found to b e relatively small (e.g. 15% for the so dium

abundance and 3% for the photometric measurements). However, the systematic error caused by the laser itself

could b e very large (e.g. 50%). Moreover, the atmospheric transmission could also a ect the absolute return ux

measurements. Therefore, new so dium return exp eriments with simultaneous measurements of laser frequency and

atmospheric transmission are required to estimate p ossible systematic errors in previous measurements.

During the Septemb er run, we monitored the laser frequency with a Fabry-Perot interferometer and a Edmund

CCD camera. Wehave also measured the atmospheric transmission through observing several standard stars at

di erent airmass during the same observation run.

Table 1 shows the measurements of simultaneous absolute return ux from linearly and circularly p olarized so dium

laser b eams and so dium column density from the March, May and Septemb er runs, 1997, as well as the observation

time and airmass and corresp onding R magnitude of the laser arti cial stars. The absolute so dium laser return ux

is de ned as the ux measured without the atmospheric transmission loss. The atmosphere transmission was T 0:9

at the Zenith during the Septemb er observation run. The same atmosphere transmission of T = 0.9 is assumed for

the March and May observation runs.

Table 1. Simultaneous Linearly and circularly Polarized Laser Return and Column Density Measurements

Polarization Time (MT) Airmass Absolute Return Flux at Zenith N(Na) at Zenith R mag./W

5 2 9 2

(10 Photons/m /s/W) (10 atoms/cm )

linear 1h13m, 3/23/97 1.16 4.0 2.20.5 11.4

linear 3h18m, 5/20/97 1.17 8.2 3.00.5 10.6

linear 3h23m, 5/20/97 1.17 11.7 4.30.7 10.2

linear 3h33m, 5/20/97 1.18 10.1 4.60.7 10.4

linear 3h39m, 5/20/97 1.18 10.6 4.30.7 10.3

circular 12h32m, 3/23/97 1.07 4.9 1.70.5 11.1

circular 1h16m, 3/23/97 1.21 4.5 2.10.4 11.2

circular 1h26m, 3/23/97 1.21 5.9 1.90.5 10.9

circular 1h55m, 3/23/97 1.28 5.7 2.70.4 11.0

circular 2h45m, 5/20/97 1.12 14.0 4.50.7 10.0

circular 3h08m, 5/20/97 1.14 11.3 3.30.6 10.2

circular 4h04m, 5/20/97 1.26 8.6 3.60.7 10.5

circular 4h08m, 5/20/97 1.26 5.8 2.70.5 11.0

circular 4h14m, 5/20/97 1.28 12.6 5.10.9 10.1

circular 4h18m, 5/20/97 1.29 13.8 5.80.9 10.0

circular 0h32m, 9/13/97 1.00 12.6 3.80.6 10.1

circular 0h49m, 9/13/97 1.41 11.5 4.60.7 10.2

circular 0h59m, 9/13/97 1.41 12.1 4.40.8 10.2

circular 1h28m, 9/13/97 1.41 12.8 3.40.5 10.1

Figure 3 shows the relationship b etween the absolute laser guide star ux and so dium abundance at the Zenith.

The backscatter from circularly p olarized b eams obtained from three di erent observation runs is prop ortional to

so dium column density. The absolute return measurements from the Septemb er run are consistent with previous

ones. Figure 3 also shows theoretical prediction of the absolute laser return ux (the dashed line) based on the

following estimate

1:5; (2) N = N

r t

1 18 1

where N is backscatter in unit of photons s , N =3:0 10 photons s is the total output ux of 1 watt so dium

r t

laser, A is the photon collector area. H = 90 km is the height of the so dium layer ab ove the telescop e, = N ,

c P Na 20

3/23/97 data 5/20/97 data 9/13/97 data 0

0246

Figure 3. Absolute ux of so dium laser returns of circularly p olarized b eams vs so dium layer abundance at Zenith.

12 2

where N is the so dium column density, and the p eak cross section of the D hyp er ne =8:8 10 cm is

Na 2 P

applied b ecause < 10 MHz line width for the cw dye laser tuned to the hyp er ne p eak is very narrow compared to

the 1.19 GHz FWHM of the D hyp er ne line (Happ er et al. 1994). The angular dep endent scattering factor, 1.5, for

the backward is also used in equation (2) (Jeys 1991). The theoretical predicted values are larger than the measured

values from the circularly p olarized laser b eams. This result should b e exp ected b ecause the laser frequency was

found not always lo cked on the frequency corresp onding to the p eak of the D hyp er ne structure, whichwould

result in less return ux.

The laser frequency instabilitywas monitored byaFabry-Perot interferometer. Figure 4 shows the typical

interferogram from this interferometer recorded byanEdmund CCD camera. The interferograms were recorded

and used to measure the simultaneous laser frequency.We found that the laser frequency mainly hopp ed among

four adjacent mo des randomly. The frequency di erence b etween the two neighb or mo des is 0.276 GHz, whichis

determined by the ring laser cavity size. The laser mo de hopping rate is higher than 3 Hz. Once the so dium laser

mo de hopp ed from the mo de with frequency corresp onding to the p eak of the D hyp er ne structure to other mo des,

the return intensityshouldbemuch less b ecause of the smaller cross-section asso ciated with the other mo de frequency

(Milloni & Telle 1996). If the typical kinetic temp erature of the so dium layer, T = 210 K, is assumed (Ge et al.

1997; Happ er et al. 1994), then the e ect so dium cross section for the Septemb er return measurements is 2/3 of the

p eak value.

If the correcting factor of 2/3 is applied to the Septemb er so dium return results, then a laser guide star with R =

6 1 2

9.8 mag. or absolute ux of 1.7110 photons s m , is exp ected to b e formed from 1 watt of pro jected circularly

p olarized so dium cw laser when the so dium laser frequency is lo cked on the p eak of the D hyp er ne structure and

9 2

the so dium layer abundance is at its mean value of N(Na) = 3.710 cm at our latitude (Ge et al. 1997). This

value is 2.0 times that we rep orted in our previous pap er, is consistent with the prediction from theoretical studies 1

0.8

0.6

0.4

0.2

0 -0.5 0 0.5 1 1.5

Relative Frequency (GHz)

Figure 4. (a). Interferogram from a Fabry-Perot etalon to monitor laser frequency jitter during the so dium laser

return exp eriments. (b). Laser frequency distribution function. The so dium dye laser mo de separation with the ring

cavity is 0.276 GHz. The zero frequency corresp onds to the frequency of the p eak cross-section of the so dium D

hyp er ne structure.

including the Earth's magnetic eld and optical pumping e ects (Milonni 1997, private communication). The main

di erence b etween this result and previous one (Ge et al. 1997) is that wehave included the correcting factor caused

by the laser frequency jitter, as well as the measured atmospheric transmission into the consideration to reduce

systematic errors in the nal value.

The re ned simultaneous measurement results provide a reliable base for the design of next generation so dium

laser guide star AO systems. Based on these results, the detected so dium laser return photon numb er for a collecting

ap erture with an area of A (m )intheintegration time (milliseconds) is

N = 1710T P A; (3)

when P watts single mo de so dium cw dye laser, lo cked to the D p eak cross section frequency, is launched to the

so dium layer. The is the total collecting system eciency including sky and collecting system transmission and

detector quantum eciency. If the return photons are collected bya Shack-Hartmann wavefront sensor for wavefront

correction, then the total wavefront reconstruction error for each subap erture is (see Sandler et al. 1994 for details)

2 2 2

4 G FWHM 4n 0:589

2 2 2

= ( ) (1 + )( ) : (4)

rec

N =d N

where N is the numb er of detected photons in each subap erture which is describ ed in Eq. (3), FWHM is the so dium

sp ot size viewed by each subap erture, d is each subap erture size, n is the detector readout noise. Therefore, the

more photons each subap erture can collect, the less the resulting wavefront reconstruction error is. On the other

hand, Eq. (4) also demonstrates that the wavefront reconstruction error strongly dep ends on the so dium sp ot size.

For example, a doubling of the sp ot size would require a quadrupling of laser p ower to maintain the same wavefront

correcting p erformance. Therefore, it is very imp ortant to build a so dium laser b eam pro jector which can provide

the so dium layer sp ot size as small as p ossible.

Figure 5. Diagram of the so dium laser b eam pro jector as it was mounted on the MMT during the 1997 March,

Mar and Septemb er runs.

3. SODIUM SPOT SIZE AND SODIUM BEAM WAIST MEASUREMENTS

Figure 5 shows the schematic drawing of the so dium laser b eam pro jector, whichwas used for measuring the so dium

b eacon size and so dium waist during the Septemb er run at the MMT (Jacobsen 1997, Ph.D. dissertation for details).

The top primary pro jector pair (PPP) is a compact telephoto design with nite conjugates. The diameters of the

top plano-convex BK7 lens and the second plano-concave SF5 lens are 48 cm and 25 cm, resp ectively. The fo cus

lens, L3, a 2 inch commercial achromat with a fo cal length of 250 mm, is lo cated 340 cm b elow the PPP. Because the

guide telescop e secondary o ccupies the space on the telescop e axis, the PPP had to b e mounted 50cm away from the

axis. In addition the guide telescop e primary, its cover and supp ort structure comprise a signi cant obstacle to the

b eam path. The lightmust b e broughtvertically from the elevation axis past the guide telescop e supp ort (Figure

5). It is in this leg that L3 and the pupil diagnostics camera suite are lo cated. Two large mirrors mounted on rigid

steel towers are used to transfer the b eam around the guide telescop e and its cover and into the PPP.

Below the second of these mirrors is a long optical rail mounted vertically.L3ismounted to this optical rail.

Also on this rail are two, 2 inch b eam-splitter cub es used to feed a diagnostics b ox, and a variable iris lo cated at

the entrance pupil of the pro jector. A pupil diagnostics b ox is lo cated next to the vertical optical rail. The cameras

in this b ox provide real time alignment and laser quality information, and a dio de provides `p ower in the bucket'

measurements.

Below the vertical optical rail, mounted on the elevation axis of the telescop e is the rapid tip/tilt mirror, whichis

lo cated 1 m b elow the actual entrance pupil. This leads to a small amount of cross coupling b etween image motion

and pupil lling. The tip/tilt mirror, controlled by the wavefront sensor computer, is capable of 1arcsec motions at

a rate of nearly 700Hz. In this way the global jitter of the laser can b e eliminated.

The relay system consists of a series of four mirrors that bring the laser b eam from the laser ro om up to the

elevation b earing of the telescop e, then sending the b eam down the elevation axis of the telescop e to the rapid tip/tilt

mirror. The rst mirror of this relay system, the one nearest to the laser, has a slow tip/tilt capability, and is used

to ensure prop er pupil lling. Also included in this relay system is a remotely activated shutter connected to the

electronic airplane \watching dog". This shutter is used to blo ck the b eam in case of aircraft passing near the b eam.

Near the laser itself is the p olarization control system and the b eam expander. The p olarization control consists

of a MgF2 crystal with tip/tilt. The p olarization control for the current system is run manually with real time

feedback from the p olarization detector. Also on the laser b enchisavariable b eam expander. The b eam expander

consists of two p ositive lenses mounted on an optical rail. By varying the spacing and slightly adjusting the fo cusing

lens on the vertical optical rail the pro jected b eam waist can either b e variedupordown to match the pro jected

b eam waist to the optimal waist.

The p erformance of the current b eam pro jector are mainly considered in two areas. The rst is amount of energy

transmitted from the laser to the sky, and the second is how tight a sp ot the pro jector generates on the sky.

The current pro jector has seven re ective surfaces and 18 refractive surfaces. Most of the mirror surfaces are

coated with protected silver coatings and most of the refractive surfaces are coated with broadband coatings. When

the pro jector was rst installed on the telescop e in 1995 the total system transmission was measured at b etween

70Since then some of the re ective surfaces have degraded signi cantly, sp eci cally the large silvered mirrors on the

telescop e structure. In addition, the top surface of L2 has gathered a signi cant amount of dust. Cleaning this

surface and recoating mirrors would require the removal of part of the b eam pro jector system. Since this pro cedure

would require several days or more of e ort to replace and realign and also the whole laser system setup at the MMT

is only for temp orary use for the FASTRACIIAO system it has b een left in its current state. As of Septemb er 1997

the total transmission, including vignetting losses, had fallen to 40

The size of the so dium b eacon can b e degraded by pro jector vibrations, atmospheric turbulence, and optical

ab errations. The initial run with the pro jector revealed a 5 arcsec elongation due to vibration of the largest mirror

in the wind. Extensive reinforcements were added throughout the system that alleviated the problem. Since then

no signi cant degradations due to vibrations have b een noted. The degradation of the sp ot size due to turbulence

cannot b e alleviated. However, the e ects of turbulence can b e minimized through appropriate waist size choice, but

some degradation is unavoidable. This degradation masks the true p erformance of the optics.

In order to measure the b eacon sp ot size it must b e viewed with a telescop e. This creates a further complication

since turbulence in the down-coming b eam will degrade the b eacon image. Therefore, in order to determine the

actual sp ot size on the so dium layer a stellar p oint spread function (PSF) taken simultaneously with the image of the

so dium b eacon is needed. This would allow the de-convolution of the PSF with the image of the b eacon. Toattempt

this, a series of exp eriments were conducted at the MMT in Septemb er of 1997. The goal of these exp eriments was

to obtain simultaneous, in-fo cus images of a star and the so dium b eacon. The fo cus of the so dium b eacon is ab out

36 mm lower than the in nity fo cus. Since it is vitally imp ortant that b oth images b e in fo cus, an instrument called

\co-fo cal b ox" was constructed for this run that can intro duce 36 mm of extra path length for the light from the

so dium b eacon (Jacobsen 1997).

In the Septemb er run, 1997, the rst half of the run was dedicated to collecting more so dium return strength

data describ ed in the previous section. During the second half of the run, a series of observations were made at the

MMT to observe the correlation b etween the b eam waist size and sp ot size and to obtain data on the size of the

so dium sp ot generated by the pro jector, optimizing the pro jector for the smallest sp ot.

The variable b eam expander was used to vary the pro jected waist size b etween approximately 19 cm and 36 cm.

This range runs across the optimum for average seeing conditions at the MMT. Seven settings were used for the b eam

expander. The b eam pro le was determined bymoving a photo-dio de across the pupil and measuring the output as

a function of lo cation. For this purp ose a wo o den plate with a series of evenly spaced, pre-drilled holes was used to

p osition the dio de. From these pro les the approximate waist was determined. These values are only approximate

since the ickering of the laser made accurate measurement dicult.

A series of exp osures at various expander settings were then taken with a natural star in the eld-of-view of the

Ap ogee CCD camera. This was done using only mirror E, which has the b est imaging quality of all the primaries.

Figure 6. Comparison b etween the data obtained from the MMT and simulations. Curve (a) shows the average,

raw image sizes of the so dium b eacons for various pro jected waists. Curve (c) shows the average sizes of the PSF

star. Curve (b) is the de-convolved sp ot sizes of the so dium b eacons. Exp osure times were b etween 100 and 200 ms.

Curve (e) is the theoretical instantaneous sp ot size for r = 15 cm measured from the PSF star images. Curve(d)

is the simulated curve for a 100 ms exp osure with 1.0 waves of defo cus intro duced into the pupil.

The exp osure times were either 0.1 or 0.2 sec. The increase in exp osure time was necessary to comp ensate for a very

light, variable cloud cover, robbing the laser of p ower. Image sizes (FWHM) for b oth the star and the so dium b eacon

were determined by doing Gaussian pro le tting to the images using the standard IRAF package. The FWHMs of

the PSF star and the so dium b eacon are assumed to add in quadrature. Therefore, the actual width of the so dium

b eacon can b e derived from the following:

2 2

) ; (5) D (D D =

beacon

imag e

PSF

where D , D and D are the FWHMs of the so dium b eacon, apparent so dium image and PSF, resp ec-

beacon imag e PSF

tively.

The relationship b etween the waist and the b eacon size did exhibit a minimum at 25 cm near the predicted

optimal waist of 29 cm for average seeing conditions (Jacobsen 1997), with increased sp ot sizes on either side of the

minimum (Figure 6). The average r , estimated from the instantaneous star image sizes, at the time of measurements

was 15 cm. Figure 6 also shows the simulated instantaneous sp ot size r0 = 15 cm using the program describ ed in

Jacobsen's thesis (Jacobsen 1997). The data suggests that the b eam pro jector was not prop erly optimized and that

there mayhave b een ab errations present. Tosimulate the e ect of a simple ab erration de-fo cus was added to the

pupil. Curve (d) in Figure 6 shows simulation results for 100 ms exp osures with 1 wave of defo cus added to the

pro jector. Adding the defo cus drove the minimum waist size down and raised the average sp ot size. The minimum

de-convolved sp ot size obtained was 0.84 arcsec which is approaching the minimum of the r0 = 10cm curve. However,

this was b efore the optimization of the pro jector alignment conducted on the last night.

On the last night of the observing run several hours were sp ent adjusting the pro jector alignment while monitoring

the image of the sp ot on the sky. This was done in an e ort to truly optimize the p erformance of the b eam pro jector.

It was noticed at the end of this pro cedure that the laser b eacon app eared to b e strongly elongated in the direction of

6 arcsec

Figure 7. So dium b eacon images taken from two separate MMT mirrors. The image on the left is from mirror C

and the image on the right from mirror E. The arrows indicate the direction of the Rayleigh column for the resp ective

images, and the exp ected axis of radial elongation. The elongation is clearly rotated in the two images and lines up

well with the exp ected directions. The exp osure time of this frame is 0.5 s and the image size from the mirror E is

0.85 x 1.30 arcsec.

its Rayleigh column. This is the direction that one would exp ect to see radial elongation of the sp ot due to the o set

of 2.5 m of telescop e mirror E from the pro jector. Toverify that the elongation was due to the radial o set, and

not to astigmatism in the pro jector or imaging optics, a second mirror, mirror C, was op ened as well. This mirror

has a mirror-pro jector axis that is rotated 120 from mirror E. The subsequent image showed a clear rotation of the

elongation, leading to the conclusion that the observed elongation was in fact due to the radial o set (Figure 7).

Analysis of the sp ot from mirror E shows a non-deconvolved sp ot with a ma jor axis of 1.30 arcsec, and a minor

axis of 0.85 arcsec. Additional data taken with a natural star in the eld yielded an average sp ot size of 0.8 x 1.12

arcsec in the raw image (Figure 8). The simultaneous natural star image size (seeing size) is 0.56 arcsec. Therefore,

the real so dium b eacon size on the so dium layer is 0.6 x 1.0 arcsec. This represents an elongation of 0.4 arcsec,

corresp onding to an 8 km FWHM thinkness of the so dium layer. To our knowledge, this is the smallest so dium

b eacon ever pro duced.

ACKNOWLEDGEMENTS

We thank the MMT sta for their great patience and help during our FASTRACIIrun,Perry Berlind and Jim

Peters for helping collecting and reducing 60 inchAFOE raw data, Matt Cheselka for helping converting the vedeo

tap e data format to standard ts format. This work has b een supp orted by the Air Force Oce of Scienti c Research

under grantnumb er F49620-94-1-0437 and F 49620-96-1-0366.

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Figure 8. The image of the smallest so dium b eacon recorded at the MMT when seeing is 0.56 arcsec. It is obtained

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b eacon size after deconvolution is 0.6 x 1.0 arcsec. The arrow indicates the direction of the Rayleigh scattering.

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