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NBSIR 77-858 do not remove

MEASUREMENT PROCEDURES FOR THE

OPTICAL BEAM SPLITTER ATTENUATION DEVICE BA-1

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

MAY 1977

Prepared for

Aerospace Guidance & Metrology Center

Newark Air Force Station

Newark, Ohio 43055

NBSIR 77-858

MEASUREMENT PROCEDURES FOR THE

OPTICAL BEAM SPLITTER ATTENUATION DEVICE BA-1

B.L. Danielson

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

MAY 1977

Prepared for

Aerospace Guidance & Metrology Center

Newark Air Force Station

Newark, Ohio 43055

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

CONTENTS

Page

1. INTRODUCTION 1

2. THEORY OF THE BA-1 ATTENUATOR 2 3. MEASUREMENT PROCEDURES 4 3.1 Attenuation to Low Power Levels 6 3.2 A Specific Example of Attenuation 10

4. ALIGNMENT PROCEDURES 12

5. CLEANING OF BEAM SPLITTER SURFACES 13

6. ATTENUATION ACCURACY 14

6.1 BA-1 Error Analysis 14

6.2 Neutral Density Filter Error Analysis 18

7. REFERENCES 2 0

LIST OF TABLES

Page

Table I. BA-1 attenuation ratios for unpolarized radiation 2 Table II. Attenuation ratios of neutral density filters 5 Table III. S-1 beam splitter attenuation ratios. Angle of incidence

-5°, wedge angle 2°, fused silica 7

Table IV. BA-1 attenuation ratios for polarized • laser input 16

Table V. Error budget for BA-1 17

Table VI. Error budget for neutral density filters 19

LIST OF FIGURES

Page

Figure 1. Path of a laser beam in the BA-1 wedged beam splitter 3 Figure 2. Layout for BA-1 attenuator 8 Figure 3. Layout for attenuation of a YAG laser beam to low levels

v/ith the BA-1 attenuator 9 Figure 4 . Example of attenuation 11

iii

MEASUREMENT PROCEDURES FOR THE OPTICAL BEAI"! SPLITTER

ATTENUATION DEVICE BA-1

B.L. Danielson

Measurer::ent procedures are described for the step attenuation

of laser bearriS up to 44 dB using a specially constructed attenuator box (BA-1) . With the use of an additional preattenuator beam

splitter, the attenuation range can be extended to over 70 dB. The

BA-1 system is designed for use at .6328 ym, .5145 ym, and 1.05 ym.

The attenuation ratios of these wavelengths are calculated values.

An analysis of the estimated uncertainties is also given.

Key words: Attenuation; laser attenuation; optical beam splitter

1. INTRODUCTION

This manual describes some procedures for the attenuation of laser

beams to low pov;er levels v/ith equipment designed and constructed at the

National Bureau of Standards (NBS) for this purpose. This equipment consists

of a seven port attenuator box, denoted by BA-1 (for beam splitter attenuator,

model (1)), a preattenuator beam splitter tc extend the attenuation range,

and some neutral density filters. For all three of these components, the

attenuation has been specified at the following wavelengths: 1.06 ym,

.6328 ym, and .5145 ym. The BA-1 device produces step attenuation of a laser

beam to a maximum of about 44 dB . With the preattenuator beam splitter,

denoted by SI, this range can be extended as much as another 3 0 dB. The

various low level beams generated by BA-1 can be used for detector responsivity and linearity checks. This can be done in a configuration v/hich

allovr's simultaneous comparison with a calibrated power meter.

The stated attenuation ratios for BA-1 are theoretically determined from

a computer program based on Fresnel ' s equations. Many experiments were

performed to establish the validity of this program. The results of the

experiments vrere always within the experimental errors of the measurements

.

Since the experimental uncertainties in our case v;ere relatively large, we

have stated only the theoretical values. These results should apply to any

attenuation system similar to BA-1 which uses quartz beam splitters

.

The layout of BA-1 is particularly well suited for use with absorption

filters for fine tuning the attenuation. However, the filters must be calibrated experimentally at each wavelength used. The errors associated with
Table I. BA-1 attenuation ratios for unpolarized radiation.

(This table should be used if laser polarization is unknown .

)

Beam Ratio

Relative to

m=0 Beam 1 . 0 ym .6328 ym .5145 ym

lotai Max.

Estimated , , Uncertaxnty

% (m=0)/(m=-l) 27. 72 26.96 26.50 3.5

(m=0)/ (m=+l) : \ 29. 68 28 . 91 28.45 1.5

(m=0) / (m=2) ' 881.1 835.6 809.2 1.9

(m-0)/(m-3) 26, 170 24,150 • 23,020 2.5

(m=0)/(IN) .9388 .9320 .9309

^^^See section 6.1 for a discussion of these uncertainties

.

this calibration are large, as is demonstrated here with a set of glass

neutral density filters. We therefore do not recommend the use of filters in

applications where the highest accuracy is required.

By way of introduction to the measurement procedures, the theory underlying the BA-1 device is given along with suggested alignment and cleaning

instructions

.

2. THEORY OF THE BA-1 ATTENUATOR

Details on the theory and use of wedged beam splitters and glass neutral

density filters are given in separate publications [1,2].^ Here we will

refer only to the salient points relevant to the BA-1 device.

The heart of the BA-1 attenuator is a supersmooth quartz beam splitter^

wedged at an angle of 2° and oriented at an angle of incident of -8.71° as

^Figures in brackets indicate the literature references at the end of this

paper

.

^The beam splitters used in this work had the following specifications:

optical quality fused silica, surface figure A/4 at .6328 ym, wedge

2.00 + .10 degrees, and smooth to 2 nm rms surface finish. The

beam splitters in BA-1 and SI are identical.

2
M =0 M =2 M = 4

Figure 1. Path of a laser beam in the BA-1 wedged beam splitter

3
illustrated in figure 1. This angle of incidence is chosen so that the

emerging beams are separated by angles which are approximately equal. Each

time the incident beam undergoes a reflection at a surface of the beam

splitter, it is attenuated by a factor of about 30 (14,7 dB) . The- exact

ratios are given in table I. The various emerging beams are identified in

the text (and on the BA-1 box) by the order number which represents the

number of reflections the incident beam has undergone in the beam splitter.

It will be noticed from figure 1 that there are two beams (the +1 and -1)

associated with one reflection. The plus and minus signs are arbitrarily

assigned to the reflections off the back and front of the beam splitter

respectively.

The BA-1 box is constructed so that absorbing glass neutral density

filters can be put in any of the low level attenuated beams without disturbing the alignment. The measured attenuations of these filters are listed in table II. The ports are located in the box so that if the input

beam, the ra = 0 beam, and one reflected beam (e.g., m = -1) are centered in

their respective ports then the other less intense beams will automatically

be aligned in their assigned ports. This alignment is dictated not only by

reason of convenience in locating the various attenuated beams but also by

the fact that attenuation ratios are a function of angle of incidence on the

beam splitter. The low level attenuated beams may be used at any convenient

distance from the ports.

The beam splitters are used as attenuators at high intensity levels.

There is negligible absorption in quartz at the calibrated wavelengths.

Damage thresholds in excess of 10 GW/cm"" have been reported [3]. At very

low power levels, the wedged beam splitter is less satisfactory due to

alignment difficulties. The glass neutral density filters complement the

beam splitters since they can be inserted into low power beams without

disturbing alignment but cannot be used at high intensity levels (greater

2 than a few tens of mW/cm ) without changing their attenuation characteristics . It should be noted that a neutral density filter should not be used in

any configuration where a surface reflection could affect measurements on a less intense beam. That is, the filter should be inserted only in the

lowest power beam used.

-

. 3 . MEASUREMENT PROCEDURES

Before considering the details of measurement techniques, a general

overview of our measurement philosophy may be in order. We wish to generate

low level beams of known power from a laser (cw or repetitively pulsed)

wnich can emit up to a few watts of average power. For high output powers

4
(a) Table II. Attenuation ratios of neutral density filters.

. ^ . Total Max. Estimated Measured Density ...

1 (5) Nominal

Density 1.06 ym .6328 ym .5145 ym

Uncertain

%

.2 .424 .221 .208 14.6

.3 .630 .331 .317 15.0

.4 .849 .435 .417 10.6

.5 .738 .526 .520 11.0

.6 .674 .611 .628 (c)

.7 .999 .896 .922 . (c)

.8 .899 .804 .825 21.5

.9 1.02 - .921 .941 . (c)

1.0 1.10 .995 1.02 21.0

2.0 1.32 1.87 1.98 20.7

3.0 1.95 2.89 3.06 20.5

Note the measured values differ significantly from the nominal values.

For example, at 1.06 ^im the density of the nominal .4 is greater than

the nominal .6.

See section 5.2 for a discussion of these uncertainties.

The attenuation uniformity of these filters was not measured.

5
like this it is usually desirable to preattenuate this output to a few milliwatts or so. The power or energy measurements are then made at this reduced

level with a suitable detector of knov/n response. This preattenuation avoids

excessive heating or damage to the detector, or filters if used, which could

adversely affect measurement accuracy. Further attenuation of a known amount

is made with the higher order reflections from the BA-1 box. We monitor the

power on one of the output beams (usually m = 0) at a convenient level of a few milliwatts, and from the tabulated attenuation ratio we calculate the

power in the other less intense beams. If desired, additional attenuation

can be made with the insertion of the calibrated neutral density filters

provided. The attenuated beams can then be used for determining the responsivity and linearity of sensitive detectors.

The calibrated detector may be either a power meter or a calorimeter.

A calorimeter is basically an energy measuring device, and to infer average

power a gated beam is required; that is, the energy is injected into the

calorimeter for a known period of time. The NBS standards of laser power

and energy are calorimeters [4] , and generally these devices are capable of

greater accuracy than power meters. However, they require additional equipment and detailed data analysis [5]. We will assume here that only a calibrated power meter is available for use with the BA-1 attenuator system.

3 . 1 Attenuation to Low Power Levels

Generation of low power level beams may be accomplished by an experimental arrangement similar to that illustrated in figure 2. This configuration provides step attenuations relative to the m = 0 beam, as given in

table I. For intermediate attenuations, neutral density filters may be

inserted in any of these beams (at the cost of some additional uncertainty)

.

For high power lasers, and particularly high power YAG lasers, the arrangement of figure 3 may be more suitable. The function of the mixer S2 and

mirrors Ml, M2 , and M3 is described in detail in section 4 on alignment

procedures. For attenuation ratios up to about 60 dB the optional beam

splitter SI may be removed and mirror Ml made totally reflecting. To reduce

the power entering the BA-1 box, the m = 2 beam of SI may be used for an attenuation of about 30 dB. Alternatively, mirror Ml may be replaced by 81

and the m = -1 reflection used for about 15 dB of attenuation. The choice

of configurations will depend on output power of the YAG laser and desired

final power levels. Ordinarily, it is not necessary to know the exact

amount of preattenuation produced by SI since the power will be measured

downstream from this point. Nevertheless, for reference a typical set of SI

beam splitter ratios (for -5° angle of incidence) is given in table III.

6
Table III. S-1 beam splitter attenuation ratios. Angle of incidence

(a) wedge angle 2°, fused silica.

Beam Ratio

Relative to

Incident Beam 1.06 ym .6328 ym .5145 ym

(IN)/ (m=0) 1. 071 1.073 1.074

ClN) / Cm=-1) 29.68 28 . 91 28.44

(IN)/(ra=+l) 31.79 31.01 30.55

(lN)/(m=2) 943.5 896.4 869.1

(lN)/(m=3) 28,010 25,910 24,720

The uncertainties in the beam ratios are approximately the same as given in table I.
6
Figure 3. Layout for attenuation of a YAG laser beam to low levels

with the BA-1 attenuator

9
After the BA~1 box is aligned (see section 4) with the incoming laser

beam, wa can make detector linearity checks and cw responsivity determinations at a number of power (or energy) levels. A specific example is

illustrated in the follov/ing section.

3 . 2 A Specific Example of Attenuation

Let us assume we have a cw YAG laser with an output power of 20 W and

that we wish to produce an attenuated beam of about 10 yW for the purpose of

measuring the responsivity of a detector at this level. This requires approximately 63 dB of attenuation. To accomplish this we set up the BA-1 box

with the SI beam splitter preattenuator as shown in figure 4. Table III

indicates that the m = 2 beam emerging from SI will be attenuated by a factor of 944 (30 dB) . After undergoing losses in Ml, M2 , and S2 we can expect about 10 mW input into the BA-1 box. This is a convenient level.

The pov/er is monitored on the m = 0 beam, and all other power levels are aetermined relative to this reading. The power P^ in the mth order beam is

found from table I as follows:

P_^ = P^/27.72 = [3.606 x lO"^ + 1.3 x 10~^]P^

P,-, = P /29. 68 = [3 . 369 x 10~^ + 5.1 x 10~^]P +1 o o

• P„ = P /881.1 = [1.135 X 10~^ ± 2.2 x 10~^]P

2 o' ^ o

P^ = P /26,170 = [3.825 x 10~^ + 9.6 x 10~^]P

3 o o The output from port 2 (m 2) will give about the desired power level with

P^ = 10 mW. Linearity of response of the detector can be ascertained by use

of neutral density filters and other output beams to provide finer steps of

attenuation. The calibraLed filter attenuations are given in table II.

Large attenuation ratios, such as those illustrated in this example,

require proper precautions to avoid scattered light. In figure 4 a baffle

and light traps are shown, which help in this regard. All unused higher

order beams from Si and S2 must be suitably blocked. It also helps to

pnysically separate the components to take advantage of the inverse square

law of scattering. The power meter should be placed at least a meter behind

BA-1 and tilted a few degrees so that the specular component is not reflected

back into BA-1.

10
M2 /s Steering

Mirror

S2 \/ A Mixer

Baffle

BA-1 Attenuator

Yog Laser

1.06 ^nn

Spatial

Filter

Preattenuator

SI

Trap

Steering

f^'^ Mirror

Power

Meter

Figure 4. Example of attenuation

11
" " 4 . ALIGNMENT PROCEDURES

Alignment of the BA-1 attenuator system in figure 2 at visible v/avelengths is not difficult. As mentioned previously, if the input beam, the

m = 0 beam, and the m - -1 beam are centered in their ports on the BA--1 box,

then the system is aligned. This can also be done at 1.06 ym, but requires

care at low power levels.

One of the main concerns in the design of the BA-1 optical system was

to pr';-'duce a device v/hich could be aligned easily at low infrared (ir)

intensities. The easiest method of locating all the beams entering and

emerging from BA-1 is to make the ir beam collinear with a visible red beam

from a nominal 2 mW HeNe alignment laser. This is not essential as long as the attenuated beams are sufficiently intense to be seen by an ir viewer,

but is very convenient nonetheless. Overlapping the visible and ir beams is

easily accomplished on a large (2m x 3m), flat, preferably magnetic, table

(or several tables) as follows (refer to figure 3)

:

a) With the BA-1 box temporarily removed, set up an HeNe laser and

mixer beam splitter S2 so that a red beam is generated approximately 11.1 cm above and parallel to the table top. A height

gauge is essential for accurate v/ork . The mixer S2 is specially

coated so that it reflects 95% of the red beam and transmits about

85% of the 1.06 ym beam.

b) Place the retro-mirror M3 in the red beam at the extremity of the

available working space and direct the beam back on itself so that

it returns exactly to the HeNe laser. This is a trivial operation

if M3 is in a gimbal mount.

c) The red beam from M3 will also emerge from the mixer S2 in the

direction of the steering mirror M2 . The mixer beam splitter S2

is wedged at about 1/2 degree, and the beam, of course, tends to

refract toward the base of the mixer, so that the wedge of the

latter must be properly oriented in its gimbal mount to keep the

beam at a constant distance from the table top (base of wedge to

the right in figures 3 and 4)

.

d) The red beam will now be collinear with the ir beam if the two

coincide at mirrors M2 and M3 . This is easily accomplished by

putting a piece of lens tissue over each mirror in turn, using an

ir viewer to observe the spots, and adjusting the upstream mirror

in each case to make the spots overlap,

e) Now that the red and ir beams are collinear the ir beam is blocked

off, and further alignment is done with the red beam. This consists

of making sure that the emerging beams are centered in their ports

and are in the proper plane above the table top. Most of this

adjustment has been done on the BA-1 box before delivery.

12
f) The retro-mirror M3 is nov/ reraoved and replaced v;ith a pov/er

meter

.

Note #1: Due to dispersion in the prisms, the red and ir beams v/ili not

exactly overlap on all beams. The maximum difference in overlap of beam

centers is about 1.3 mm at 1 m distance from BA-1.

Note #2: Once the BA-1 box is inserted in the collinear beam, the retromirror M3 will no longer be in the proper location to reflect the red beam

back on itself. If further checks are desired to insure overlap of the red

and ir beams, M3 will have to be moved slightly and readjusted as before.

5 . CLEANING OF BEAM SPLITTER SURFACES

As indicated earlier, experimental work at NBS indicates that scatter

from the beam splitter surfaces due to surface roughness, dust, and general

contamination can have a significant effect on the intensity in the m = 4 beam. Significant scatter occurs even shortly after the beam splitter has

been cleaned. Surface contamination due to smoke, aerosols, and oil mist

from vacuum pumps can aggravate this problem. For this reason, measurements

on the m - 4 are noL reooauuended . However, for the super smooth beam splitter

presently in use in BA-1, the m 3 and lower order beams seem to be stable

with time in a normal laboratory environment, at least for many months.

Should cleaning of the beam splitter be necessary, we recommend the

technique described by Heinisch [6] as follows:

a) Soak the element for several hours in hot detergent solution (made

from filtered, distilled, deionized water).

b) Rinse with filtered, distilled, deionized water (hereafter referred

to as water) and then gently rub with a saturated cotton ball

until the entire surface has been covered.

c) Rinse the surface with water and examine for a v/ater break where

the water does not maintain a uniform continuous film. If some portions do not pass the water break test, repeat b) and c) until

they do.

d) The surface covered with water is blown dry with a jet of dry,

oil free nitrogen. This is begun at the highest point and con- tinued with horizontal sweeps to the bottom of the surface. Care

should be taken not to permit water droplets from the edge to flow

across the dry area.

e) Inspect by illuminating the surface with a collimated beam of

visible light with approximately the spectral distribution and

illuminance of sunlight. The surface should be viewed in a darkened room against a black background.

f) If step e) shows the surface to be clean, proceed to measure

scatter levels; if not, repeat steps b) - e)

.

13
The glass neutral density filters

soiled v/ith a fingerprint or something

above can be used. ,

should not require cleaning, but if

similar, the same procedure outlined

6 . ATTENUATION ACCURACY

The attenuation ratios of the various beams emerging from the BA-1 box

have been calculated theoretically for an unpolarized laser and listed in

table I. The attenuation ratios for the preattenuator SI have also been

calculated for an angle of incidence of -5° and listed in table III. The

optical densities tabulated in table II were measured experimentally v/ith

pyroelectric detectors equipped with a digital readout. The uncertainties

associated with these values will be analyzed.

6.1 BA-1 Error Analysis

The attenuation properties of BA-1 are determined solely by a 2 degree

wedged fused silica beam splitter. This is a stable, well-characterized

device which allows us to calculate most of the expected errors contributing

to the attenuation uncertainties of the various m orders. An additional

systematic error is due to the incoherently scattered radiation at the

surface of the beam splitter, which will be considered separately.

The m^^ order attenuation ratio R is a function of the index of refrac

m

tion n, wedge angle w, angle of incidence A, polarization P, and temperature

T;

= f (n,A,B,P,T) . (1)

This function cannot be put in closed form, but is easily programmed on a computer (see [2]) . The systematic ^ error 6Rmmin R caused by12a systematic

error in variable x_^ , 6x^, is given by

• 6R = 1^ 5x. (2) m 3x . 1

1

g f where the quantity 5—— represents the usual rate of change in f with respect

1 to the variable x^ at the operating point of f, and the other j 7^ i variable

being held constant. These slopes can be estimated numerically by varying

tne appropriate parameters in the same computer program that was used to

determine R^. The dx^ denotes the estimated uncertainty in the value of

variable x . . This procedure is used with all the x. variables. A conserva- ,1 1 tive method of determining total uncertainty is to sum the individual errors

of the constituent variables, or

m _ 1 3f

m m 1=1 I 1

14

(3)
v.'nere the j variables are given in eq . (1) / and vv-e have expressed the total

estimated uncertainty as a fraction. The estimated uncertainties dx . were

computed as follows:

Wedge angle w . The wedge angle inaccuracy dw was taken to be .06°.

This figure represents the 95% confidence limits on wedge angle measurements.

Angle of incidence A . The error in the angle of incidence can be kept

less than dA = .38°. A variation of this magnitude v/ould be evident as a

2 mm shift in the position of the laser beam in one of the BA-1 exit ports,

V7hicn is easily observable and can be corrected by realignment.

Index of refraction n . The index of refraction used in our computer

program was taken from the data of [7 J at 293 K. This work documents observed sample- to-sample variations in n . In particular, the maximum variation of n for samples of fused silica obtained from different ' sources v/as

about + .000028, and we assumed dn in our error analysis to be of this

value.

Polarization P . The data in table I are for unpolarized (or pure circularly polarized) radiation. Table I should also be used if the polarization state is unknown. The maximum polarization error occurs for either

corapletely vertical or completely horizontal polarization. These effects

can be calculated from the computer program. If the polarization is plane

polarized in either a vertical or horizontal direction, then the attenuation

ratios in table IV can be used to yield an improved accuracy. Hov/ever, we

take the view that, for BA-1 to be a useful device, we should not require

any information on input laser polarization. In this case table I should be

used. Polarization uncertainties will often dominate the overall uncertainty

in attenuation ratios

.

Temperature T . The beam splitter attenuation ratios are dependent on temperature since n is a function of T. This dependence is given approximately by the relation [7]

1^ = 10"^ (4)

or |dn| ^ 1Q~^ for | dT | =^ 10 k around 293 K.

Scatter. This contribution to the total uncertainty in R must be con- ^ m sidered separately from the other variables since it cannot be accurately

calculated. Experiments to measure the magnitude of the scatter are described in reference [2] . The maximum observed variation of R due to this

effect was 15% on the m = 4 beam. The importance of scatter diminishes as

tne order number ra decreases.

The above BA-1 uncertainties have been listed in table V. As stated

before, we do not recommend use of this m = 4 beam due to the large scattering errors. For other orders it can be seen that the total estimated

uncertainties are less than 3.5%.

15
Table IV. BA-i at tenuation ratios for polarized laser input

.

Vertical Polarisation

Beam Ratio

Rp 1 n tive to

m=0 Beam 1.06 ym O 0 Q 1 Im .DxHJ pra

Total Max.

Estimated , . (a) unpertaintv

%

(m=-0)/(m=-l} 26.79 OA O ZO . U

J

O Q A A Zj> . OU .11

(in=0)/(m=+l) 29.25 0 Q /. Q 0 Q AO Zo . UJ .04

(m=0)/(m=2) 864.9 OZU . 4 .08

(m=0)/(m=3) 25,680 23,710 22,600 .69

(m=0)/(lN) .9322 .9304 .9293

Horizontal Polarization

Beam Ratio

Rp 1 a t i VG t o m=0 Beam 1.06 pm

/: n 0 O 1 , .oJZo pra . 5145 ym

Total Max.

Estimated , . 13.) Uncp rf p in t V

%

(m=0)/(m="l) 28.68 0 "7 O O O "7 /.A Z / . 4U .11

(m-0)/(m-+l) 30.12 zy , J J Z b , o D .04

(m-0)/(m-2) 897.5 OCA O o50 , o

o o o o oZ J . O .08

(m=0)/(m=3) 26,640 24,590 23,430 .69

(m=0)/(lN) . 9353 .9335 .9325

16
Table V. Error budget for BA-1.

Percent change in beam splitter ratio,

(Absolute value at .6328 ym)

Order Number

Error

Source -1 +1

1. Index variation max. < .01 < .01 .02 .03 .04

sample variation

2. Wedge angle uncertainty < .01 < .01 < .01 < .01 < .01

3. Angle of incidence .02 < .01 .01 .01 .01

variation

4. Polarization 3.39 1.46 1.82 1.81 2,13

max. variation

5. Temperature-variation .04 .04 .07 .10 .14

± 10 K from 293 K

6. Scatter < .01 < .01 .02 .52 15

7. Total uncertainty 3.5 1.5 1.9 2.5 17.3

17
It should be emphasized that the attenuation ratios as well as the

expected errors are largely calculated values based on the computer program

described in [6] . Many experiments have been performed at NBS to test the

validity of this program. Some of these experiments are described in [6]

and [7] where theory and experiment are compared. We have no experimental

evidence to indicate that our theoretical predictions are incorrect. Because

we believe the experimental determination of attenuation ratios is inherently

less accurate than calculation, only the theoretical values of are tabulated here. The only experimental measurements made on BA-1 v/ere to check

that BA-1 was a mem.ber of the set v/hich possesses the characteristics assumed

in the computer program. That is, we measured the wedge angle and at one wavelength to assure that the beam splitter material was fused silica.

Tne measured R was within the 95% confidence limits of the predicted

m computer value

.

The uncertainties in table V are calculated at .6323 ym. The changes

in these values for other wavelengths are negligible.

6 . 2 Neutral Density Filter Error Ana lysis

The system.atic errors v;hich can be calculated for the absorbing glass

neutral aensity filters are described at length in [7] and will not be

elaborated on here. They are summarized in table VI along with their estimated maximum values. In addition we have tabulated the measured filter

uniformity. This was checked with a 1 mm diameter HeNe laser beam, and the

maximum edge-to-edge density excursions are listed. The measured attenuation imprecision varies from filter to filter and is generally greater for

tne higher densities. The values listed in table VI represent 95% confluence limits of measurements made on the respective filters. The systematic

measurement inaccuracy is associated with the non-linearity of the pyroelectric detectors and is estimated by the designer of these instruments at

about 4%. As before, the total uncertainty is conservatively figured as the

linear sum of the various systematic and random errors and is given in the

bottom line of table VI. Obviously, these errors can be reduced if care is

exercised in the use of these filters in any practical experimental con- figuration. The bottom line uncertainty represents the maximum or worst

case estimate of error. These stated values were not determined for all

wavelengths, but the wavelength dependence is expected to be negligible.

It can be seen that the uncertainties are, in general, much greater

than those of BA-1, and consequently these filters should not be used in

applications requiring the greatest possible accuracy.

18
Table VI. Error budget for neutral density filters.

Percent change in attenuation at .6328 pm.

Knovv-n ^ Error ^^^^^

Source .2 .5 1.0 2.0 3.0

1. Impedance in filter 5.3 2.6 .8 < .1 < .1

(raaximun:)

2. Tilt at 3° angle of < .1 .1 .1 .3 .4

incidence

3. Temperature variation 3.0 3.0 3.0 3.0 3.0

± 10°C froai 20°C

4. Uniformities. :->iax. 1.0 1.3 3.6 4.8 7.0

measured variation from

average Q . 6328 \xm

5. Measureaient imprecision 1.3 0 9.6 8.6 6.1

(at .5145 \iin. measurements)

6. Systematic measurement 4.0 4.0 4.0 4.0 4.0

inaccuracy (Deviations

from linearity)

Total estimated max. 14.6 11.0 21.0 20.7 20.5

uncertainty (%)

19
7 . REFERENCES

Beers, Yardley, The theory of t.he optical wedge beaim splitter, .Nat.

Bur. Stand, (U.S.), Monogr. 145 (1974).

Danielson, B.L. and Beers, Yardley, Laser attenuators for the- production

of lev/ povvfer beams in the visible and 1,06 ym regj.ons, Nat. Bur. Stand.

(U.S.), Tech. Note 677 (1975).

Fradin, D.W. and Bass, M. , Visible and infrared laser-induced davaage to

transparent materials, Raytheon Report AD-776 804 (1974).

West, E.D.,- Case, W.E., Rasmussen, A.L., and Schmidt, L.B., J. Res. Nat.

Bur. Stand. (U.S.), 76A, No. 13 (1972).

West, E.D., Data analysis for isoperibol laser Galorirr.et:cy , Nat. Bui^.

Stand. (U.S.), Tech. Note 396 (1971).

Heinisch, R.P., Infrared mirror-scatter measurements, J. Opt. Sec. Am.

61_, 1225 (1971) . Malitson, I.H., In cerspecimcn comparison of the refractive index cf

fused silica, J. Opt. Soc. hm. 5_5, 1205 (1965).

20
•<BS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

RiRi inr;RAPHir data

SHEET

1. i-'Uhlic;ation or ri-por i no. NBSIR 77-858

2. Gov't Accession

No.

3. Recipient's Acces.sion No.

I. TITLE WD SUirriTLl-: Measurement Procedures for the Optical Beam Splitter

A ft p>n n 3 1" i nn l~)pvipp RA—

]

5. Publication Date Mav 1977 *

6. Performing Organization Code

276.08

B.L. Daniels on

8 • F'e r f or ming 0rg3.n. Report No.

. PERFORMING ORGANIZATION N'A.ME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2761171

11. Contract/Grant No.

2. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Aerospace Guidance Metrology Center

Newark Air Force Station

Newark, ^ Ohio 43055

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

5. SUPPLEMENTARY NOTES

L ABSTRACT (A 200-word or less [actual summary of most significant information. If document includes a significant

biblioStaphy or literature survey, mention it here.)

Measurement procedures are described for the step attenuation of laser beams

up to 44 dB using a specially constructed attenuator box { BA-1 ). With

the use of an additional preattenuator beam splitter^the attenuation range

can be extended to over 70 dB. The BA-1 system is desigred for use at .6328yia,

.5145 "uni, and 1.06 )jm. The attenuation ratios of these wavelengths are calculated values. An analysis of the estimated uncertainties is also given.

KEY UORDS (six to twelve entries; alptiabetical order; capitalize only the first letter of the first key word unless a proper

name; separated by semicolons)

Attenuation; laser attenuation; optical b earn splitter

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