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MAR 6 1973

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TECHNICAL NOTE NO. 340 h UNASSIGNED

Library, N.W. Bldg

AUG 16 1966

The Long-Term Performance

of Two Rubidium Vapor

Frequency Standards

341

B. E. BLAIR AND A. H. MORGAN

.Hf OP C,

*"**M <* '

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

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UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary

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NBS TECHNICAL NOTE 341

ISSUED JUNE 22, 1966

THE LONG-TERM PERFORMANCE OF TWO RUBIDIUM

VAPOR FREQUENCY STANDARDS

B. E. BLAIR AND A. H. MORGAN

Radio Standards Laboratory

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means tor making available scientific data that are of transient or limited interest. Technical Notes may be

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TABLE OF CONTENTS

Page

2. BRIEF DESCRIPTION OF THE RUBIDIUM

FREQUENCY STANDARDS 2

3. THE USFS REFERENCE BASE 4

3. 1. Function of Working FrequencyStandards and Relation to USFS 4

3. 2. Methods of NBS FrequencyCalibrations in Terms of USFS 5

4. PERFORMANCE DATA 6

4. 1. Long-Term Performance 7

4. 2. Comparison of Two Rubidium and One

Cesium (Commercial) Atomic Frequency

Standards 9

4. 3. Short-Term Stability 9

5. RELIABILITY OF Rb-1 AND Rb- 2 . ... 11

6. CONCLUSIONS. 13

7. ACKNOWLEDGMENTS. 14

8. REFERENCES............. 15

9. APPENDIX. 19

9. 1. Description of Least Squares Statistical

Program for Use With High Speed

Electronic Computer 19

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ABSTRACT

Since mid-1961 the National Bureau of

Standards has used two rubidium vapor frequencystandards as transfer or Working Frequency Standards

(WFS). The WFS provides a continuously available frequency which is periodically calibrated in terms of the

United States Frequency Standard (USFS). This paper

evaluates these calibration data over a 44. 5-month

period of time. It gives the long-term performance

of the rubidium standards in terms of the USFS, compares them with a commercial cesium-beam frequency

standard, and presents their reliability characteristics

as shown by the mean-time-between-failures (MTBF).

The calibration data are graphed with applicable tolerance limits for the between-adjustment periods. The

average standard error of estimate about least squares

lines fitted to the frequency data is about 2 parts in

10 . The rubidium standards also show a rather consistent daily aging rate of parts in 10 x

. This would

indicate that the frequency of either unit would change

a few parts in 10 uif operated continuously for one

year without any frequency adjustments.

Key Words: aging, calibration (USFS), frequency

standards, gas cells, performance

(long-term), reliability, rubidium,

stability

IV
THE LONG-TERM PERFORMANCE OF TWO

RUBIDIUM VAPOR FREQUENCY STANDARDS

B. E. Blair and A. H. Morgan

1. INTRODUCTION

In the field of atomic frequency standards the arrival of commercial

rubidium (Rb) gas cells has aroused considerable interest in what one can

expect of their long-term performance and stability. However, as pointed

out by Farmer LI 963 J, there is a lack of such data simply because of their

relatively recent appearance. Since the first two commercially -available

Rb frequency standards have operated nearly continuously over a 44. 5-

month period at NBS, we can provide the record of their operation for

appraisal and study. This paper reports primarily on such long-term

performance based on periodic calibrations with the United States Frequency Standard (USFS). Data on a third Rb frequency standard, used for

a period of 3 months in 1964, are included also.

The Rb gas cell standards have been extensively described in the

literature [Bender, Beaty, and Chi, 1958; Whitehorn, 1959; Andres,

Farmer, and Inouye, 1959; Carpenter, Beaty, Bender, Saito, and Stone,

I960; Packard and Swartz, 1962; Arditi and Carver, 1963; Reder, 1963].

These papers trace their development from the earliest prototype models

to the present-day commercially-constructed units.

This paper briefly describes the two particular Rb atomic frequency

standards used at NBS (called Rb-1 and Rb-2), and presents statistics on

their long-term stability in terms of the USFS. It also includes comparison data between the Rb standards and a commercial cesium (Cs) standard for a 6-month period of time, and briefly discusses relevant characteristics of the Rb standards, such as short-term stability and reliability

of operation as experienced at NBS.
2. BRIEF DESCRIPTION OF THE RUBIDIUM FREQUENCY STANDARDS

Early in 1961 NBS obtained the first two commercially -available Rb

atomic frequency standards which, except for short periods for repair

and modification, have operated continuously from then until the present

time. Each standard occupies nearly 3 cubic feet in a cabinet package

weighing about 100 pounds. (A later version of Rb standard is now available in which the volume, weight, and power requirements are all reduced

by a factor of 1/5 or more, and the specified performance is comparable

to the older model. ) Environmentally, the vital elements of the instrument

are well protected. Proportionally-controlled ovens maintain temperaturesensitive components within set tolerance limits of temperature, and a

triple mu-metal shield surrounds elements susceptible to external magnetic fields. A brief description of the internal functioning of these standards follows; detailed operational features are available in the literature

LAndres et al. , 1959; Packard and Swartz, 1962; Arditi and Carver, 1963 J. Basically, the Rb frequency standard consists of a 5-MHz crystal

oscillator which is stabilized by an atomic resonance of rubidium through

suitable frequency synthesizers, multipliers, and automatic frequency

control. Optical pumping and light -transmission monitoring form the

87

basis for detecting atomic resonance of Rb between the ground state

levels F = 2, M = to F = 1, M = 0. Figure 1 shows a simplified F F

block diagram of the Rb frequency standard. The heart of the rubidium

o "7 o c standard is the optical package which contains an Rb lamp, an Rb

87

filter, an Rb gas cell within a microwave cavity, and a silicon photo

cell detector.

Functional operation of the Rb frequency standard is as follows:

87

after the light from the Rb lamp is directed through the filter and gas

cells, it is detected by the photo cell. The intensity of light transmitted

through the gas cell to the detector depends on the difference between the
87 microwave excitation frequency and the Rb transition frequency. Initially, through a repetitive process called optical pumping LKastler, 1957J,

an excessive number of Rb atoms jump from the F = 1 level to the upper

F = 2 ground level, accompanied by high transparency and a consequently

higher transmission of light through the gas cell. Exciting the cavity to

the critical transition frequency between the two ground state energy levels

(approximately 6834 MHz), results in a net gain of Rb atoms back to the

F = 1 ground level and a degree of opacity to the light beam focused on

the silicon detector. To provide an error signal for correcting the frequency of the radiation driving the cavity, a low frequency (107 cps) phase

modulation of the microwave energy is applied to the cell cavity. Thus,

the light reaching the photo cell fluctuates at this frequency. A phase

detector compares the photo cell output signal with the input modulation

frequency, and the resultant phase error signal continuously locks the

quartz crystal oscillator frequency to that of Rb transition through an

electronic servo system. Thus, all of the synthesized frequency outputs

87

of the crystal oscillator are continuously related to the Rb transition

frequency. Synthesis of the Rb transition frequency from the basic 5-MHz

signal of the crystal oscillator occurs through harmonic multiplication and

subtraction using transistors and varactor diodes.

Because buffer gases are used in the Rb vapor cell to facilitate optical

pumping and to reduce the Doppler width of the hyperfine absorption lines,

the effective Rb transition frequency may be shifted either up or down,

depending upon the type and pressure of buffer gas used. Consequently,

one cannot use the modified transition output frequency as a primary

standard, but must reference it to a known frequency. On the other hand,

with proper selection of the buffer gas and its sealed-off pressure at the

time of manufacture, one can obtain any offset frequency that is required

-9

for different time scales. Fine frequency tuning, by about +5x10 , is
possible also through adjustment of the magnetic field. Thus, the limitations which preclude the use of the Rb vapor instrument as a primaryfrequency standard can prove of value if precise matching and adjusting

of output frequencies is needed.

3. THE USFS REFERENCE BASE

The defined reference for all standard frequency measurements is the

unperturbed Cs/transition frequency (F = 4, M = 0) "*-* (F = 3, M = 0) F F

of 9, 192, 631, 770 Hz at zero magnetic field [NBS, 1964]. In the United

States this primary reference frequency has been derived from NBS-constructed Cs-beam units which form the United States Frequency Standard

(USFS) [Mockler et al. , I960; Mockler, 1964], From I960 to early 1965,

the USFS consisted of two such units designated as NBS-1 and NBS-2 with

onst

-12

an accuracy of 1 part in 10 . Presently, the USFS is the newly-constructed NBS-3 which is a longer Cs-beam unit and accurate to ±1. 1x10

(1 <t value) LBeehler et al. , 1966J. These accuracy figures derive from

the RMS combination of all estimated uncertainties related to the USFS

which may cause deviations from the true cesium resonance.

3. 1. Function of Working Frequency Standards and Relation to USFS

Because the USFS does not operate continuously, the NBS established

a Working Frequency Standard (WFS), which consists of the Rb standards

and stable quartz-crystal oscillators, and provides standard frequencies

without interruption. Periodic measurements relate the WFS to the USFS.

From mid-1961 to January 1964, the Rb standards were a direct link in

the calibration and frequency control of the NBS standard frequency broadcasts LBlair and Morgan, 1965], Presently, one of the Rb standards in the

WFS contributes to the NBS-A time scale [Barnes et al. , 1965; Andrews,

1965J which, since January 1964, has given time-base control to such NBS
broadcasts. In addition, the WFS serves as a continuous frequency reference for the inter comparison of atomic frequency standards via VLF

broadcasts [Morgan et al. , 1965J and provides an internal calibration

source to the NBS Boulder Laboratories.

3. 2. Methods of NBS Frequency Calibrations in Terms of USFS

At regular intervals (usually daily except weekends and holidays) the

Rb standards were measured in terms of the USFS. The NBS Boulder

Laboratories have used two methods of frequency calibration with comparable results LBeehler et al. , 1962 J. In the initially established procedure,

called the "manual" method, the 5-MHz output of the standard under calibration directly drives the multiplier chain of the USFS. For each measurement, the operator selects an upper and lower Intermediate Frequency

(IF), equally offset from the cesium resonance center frequency, by

judging the equality of the atomic beam detector current for each condition.

For this method each reported value is the grand mean of from 20 to 50

independent measurements made over a period of 1 5 to 30 minutes. Typically, such measurements show a standard deviation less than 1 part in

10 . (It should be pointed out that the manual method has not been used

routinely since early 1963. ) In the second or "servo" method, similar multiplication and klystron

control circuitry is used as in the manual method. In this case, however,

the signal from a stable transfer oscillator becomes the input to the USFS

multiplier chain and its frequency is then stabilized by the cesium resonance by means of an electronic servo system. Frequency comparisons

are made between the transfer oscillator and the Rb frequency standard by

measuring the average period of the difference frequency between them.

In this case, the reported daily value is the grand mean of about ten 200-

second averages taken over a measurement period of about 1/2 hour.
12 The standard deviation of such values is near 2 parts in 10 for a typical

measurement period. (Standard deviations of the means of such measurements in terms of the USFS are near 5 parts in 10 [Beehler and Glaze,

1965].)

In a third measurement methods the Rb signal is continuously compared with a drift-corrected oscillator (DCO) in a phase-lock servo system

[Looney, 1 961 J. Presently, the DCO is the direct controlling link of the

NBS low frequency broadcasts from Ft. Collins, Colorado [Andrews, 1965;

Barnes et al. , 1965J. The frequency of the DCO is stable to several parts

in 10 "of the zero offset frequency and is periodically compared to the

USFS. By this method, used frequently in 1964, the daily value of the Rb

frequency was determined by integrating the phase analogue records over

24 -hour periods.

One additional method of assigning daily frequency values was used

infrequently but should be mentioned. This technique consists of continuously comparing the Rb-1 and Rb-2 signals in a phase-lock servo system.

When one standard is calibrated then, in terms of the USFS over a given

time period, a frequency value of the other standard is determined for the

same time period from the Rb-1 versus Rb-2 phase record. Such compar12

isons are made typically in parts in 10 , and we used this technique for

determining Rb-2 values for parts of periods 5 to 7.

4. PERFORMANCE DATA

This section presents the long-term performance of the Rb standards,

gives their relative stability versus a commercial cesium standard for a 6-month period, and briefly discusses their short-term stability and power

spectrum characteristics.
4. 1. Long-Term Performance

Aging effects together with random day-to-day variability most often

characterize the long-term stability of a frequency standard. Both factors

may be seen in the data plots of the two Rb standards for the period August

1961 to April 1965, given in figures 2 and 3. Summary statistics of the

least squares lines through these data are given in table 1. (These calculations were obtained with a least squares statiscical program run on a high

speed electronic computer. An appendix describes this program. ) Each

plotted point, as noted previously, is a frequency measurement in terms

of the USFS or related thereto. However, it was not always possible to

obtain a daily reading and the dotted points on the plots indicate such missing data. Since the use of any interpolated data would cause an unwarranted smoothing effect in the results, the analysis consists of actual

measurements only. On the other hand, published values were omitted at

times because of either faulty operation, service work, or scarcity of data

for a given subperiod. Such values, although true and correct, do not

contribute to the overall picture of what one can reasonably expect of a normally operating rubidium frequency standard.

From period to period a random aging (drifting) pattern for each standard is apparent in figures 2 and 3. This is more graphically shown in figure

4 where the average drift rates of Rb-1 and Rb-2 are plotted for periods

between each adjustment during 1961-1965. In general, Rb-1 shows a persistent negative drift rate, whereas Rb-2 exhibits both positive and

negative rates. During the first two or three years of operation, major

component replacements were made, and it is not known what effect this

may have had on the drift rates. Since we desired to keep the frequency

of the WFS rather close to the nominal offset, quite a few frequency adjustments also were made periodically as is shown in the data plots. (The

nominal offset is an approximation, agreed upon internationally, to the
difference in the rate of occurrence of time ticks on the universal scale

(UT2) and seconds pulses on the atomic, or ephemeris, scale (.Hudson,

1965J. Such frequency offsets corresponded to -150 x 10 in 1961,

1964, and 1965; and -130 x 10" in 1962 and 1963.) The standards show

13

an average daily drift rate of parts in 10 during the period under study.

The two curves in figure 4 show some cross correlation, but this is not

too surprising since the standards are identical and operate in the same

environment.

The variability about the least squares lines is indicated by the standard error of estimate, S , , (a measure of the scatter in the observed y/x

points in the vertical or y direction about the least squares line) [Crow

et al. , 1 960 J, shown in table 1. (The standard deviation of the frequency

values, S , is usually larger, since it includes the effects of aging. ) Table 2 gives some yearly statistics of the performance of the two standards for the 44. 5-month period. Interestingly, from year to year there

seems to be a decreasing° trend in S , . This results, perhaps, either y/x

through an improvement in measurement methods, or replacement of various components in the standards, or both. The average S , for these

12

X

standards is 1 2 to 13 parts in 10 . This figure includes the high initial

variation in 1961 and 1962 caused by component failures and their subsequent replacement. It is noted that for several periods with substantial

12 number of days, n, (n > 20), S . equals or is less than 6 parts in 10 y/x

The Rb-2 standard experienced relatively small disturbance from

March 1964 to April 16, 1965. During this period Rb-2 operated continuously and NBS made six discrete frequency adjustments, with no component alterations or replacements. Figure 5 gives a plot of these Rb-2

data with the frequency adjustments removed for convenience. A least

squares line fits the points quite well; the average negative drift rate is

13 about 8 parts in 10 and the standard error of estimate, S , , is y/x
0. 10 x 10 . There appear to be small changes in the drift rate, however, during each of the six different periods, as shown in figure 4, and

this accounts for a somewhat high average S , , for the overall period. ° y/x

Data for a later -model standard, Rb-64, were also obtained for the

period January 3 to March 30, 1964, and are shown in figure 3 and table

1. Generally, the performance statistics for Rb-64 agree well with those

of Rb-1 and Rb-2; interestingly enough, however, Rb-64 showed very little

frequency aging during this period.

4. 2. Comparison of Two Rubidium and One Cesium

(Commercial) Atomic Frequency Standards

For an approximate 6-month period (August 1962 to February 1963)

a commercial Cs frequency standard was also used as a part of the WFS.

Frequency calibrations of this standard were made and a plot of these

values, together with those of Rb-1 and Rb-2, is shown in figure 6. (For

ease of comparison, several discrete frequency adjustments were removed

from the data of both Rb standards. ) As may be seen, during this period,

Rb-2 had an average positive, drift rate; however, Rb-1 and the Cs standard show average negative rates. The oven heater of the Cs beam tube

was not functioning correctly for much of this period and what effect this

had on its apparent drift rate is not known. During this comparison period,

the Rb-2 data were the most variable with an S , of 0. 2 parts in 10 ; but y/x

the Rb-1 and the Cs standard data each show an S , of slightly more than

10 ^ /X

0. 1 part in 10

4.3. Short-Term Stability

Although the major burden of this report is the long-term performance of the Rb standards (for periods of months to years), some mention

will be made of their short-term stability. The best short-term stability
12

(standard deviation) that has been reported was near 1 part in 10 • for

averaging times of 24 seconds for each sample during an elapsed measurement period of about 13 hours [Packard and Swartz, 1962J. Packard

and Swartz Ll 9 6 Z J found that the measured stability is inversely proportional to the averaging time, due to both the low signal-to-noise ratio of

the internal crystal oscillator output signal and the phase instability of

the comparison instrumentation.

Analogue records of the continuous phase difference between two frequency standards (as given by a phase-lock servo system [Morgan and

Andrews, 1961J), provide some indication of their relative stability.

Figure 7 shows a sample analogue record which gives the phase difference

between Rb-1 and Rb-2. The slope of the trace indicates the frequency

difference rate between the two standards, and the minor variations in

the trace suggest good relative phase stability, as obtained with a servo

averaging time of nearly one minute. The standard error of estimate

about a least squares line fitted to points on this trace at 10-minute intervals is about 0. 01 usecond, corresponding to an RMS instability in fre11

quency contributed by both standards of less than 2 parts in 10 . Assuming that Rb-1 and Rb-2 contribute equally to this variation, one can compute an instability of about 1 part in 1 for each standard. Because of

the relatively long response time of the servo system (servo motor is

gear-reduced by a factor of 6000:1) and a paper speed of 6 inches per

hour, it is difficult to determine short-term stabilities for periods of 60

seconds or less from such records.

The output power spectrum of a frequency standard may also give

some indication of its short-term stability. NBS has made power spectrum measurements of a rubidium standard by comparing a multiplied 5-

MHz output to an ammonia maser reference signal at 24 GHz [Barnes,

1964; Barnes and Mockler, 1960J. These measurements gave a clean

10
center spectrum with a bandwidth at the half -power points of about 4 Hz

[Packard and Swartz, 1962J. (The comparison instrumentation, however,

may have affected these measurements to some extent, and a more realistic bandwidth is probably less than 2 Hz. ) Also, there were low level

sidebands on the carrier (40 dB below the 24-GHz signal) at ±60, ±107,

and ±120 Hz. These sidebands probably originated in the Rb standards.

Note especially that the phase modulation frequency, which provides an

error signal in the Rb standard, is 107 Hz, In addition, the noise level

of the ammonia maser spectrum analyzer is at least -47 dB below the 24-

GHz carrier [daze, 1966],

5. RELIABILITY OF Rb-1 AND Rb-2

Reliability of electronic equipment is often shown to follow an exponential frequency distribution LLloyd and Lipow, 196 Z J, such as R = exp - T/t, where

R = Reliability or probability of survival

T = Time of projected operation, hrs

t = MTBF (Mean time between failure - hrs).

A Using the calculated MTBF, t, as an estimator of t, one can show

that, for a period of one year (8760 hrs), the Rb-2 maximum likelihood

A

estimator, R, is a factor of 5 greater than that for Rb-1. Such a comparison number will vary with the time, T, due to the exponential factor;

nevertheless, it gives some measure of their relative service performance.

Table 3 gives the service performance data of the two frequency standards; bar graphs of their MTBF are shown in figure 8. Rb-2 shows over

twice the MTBF of Rb-1 and about half the number of failures. However,

the principal cause of failure, namely the tube-type lamp exciter, was

the same for both standards. After the units were modified with a

11
transistorized lamp exciter, considerably improved service resulted.

For instance, a trouble-free period of 9040 hours followed the modification of Rb-2. A time weighted average for both standards covering the

entire period of operation gives a MTBF of 5570 hours.

From the performance data over this 44. 5-month study certain statistical inferences can be made about this model of standard in general.

That is, one can derive confidence intervals which, with a stated confidence, should enclose the true MTBF. The following probability expression gives such confidence intervals:

A

2nt < t <

A

2nt

X 2n; a/

2

X 2n; l-a/2

= 90%,

where

a = 0.10

P = Probability

n = Number of failures

t = MTBF

A

t = Computed estimate of t (Total time between failures/

Number of failures)

X 2n; a / 2 = Percentage point of chi-square distribution with 2n

2

degrees of freedom; the probability of \ exceeding

CdXX this is a/2.

(NOTE: y „ is defined as for a random sample of t, LLloyd and

2n t Lipow, 1962; Carroll, 1962J. From this relationship confidence inter

vals for reliability, R, also can be found. )

12
The 90% confidence interval, then, for MTBF of this model Rb standard, based on Rb-1 and Rb-2 service data, is 3610 < t < 9930.

The failures shown in table 3 are classed as catastrophic. That is,

the standards completely stopped operation and/or it was impossible to

phase-lock the controlling oscillator to the Rb resonance. In all fairness,

we should state that at various times new components were installed in

the standards, and there are transitory effects in the frequency data before and after such installation. It was also necessary from time to time

to align the synthesizer and second harmonic amplitude. Rb-2 showed

progressively increased time between alignments. From the middle of

1962 to early 1963, we note periods of 3000 to 4000 hours between alignments. From then to early 1965, such periods increased to 6000 and 9000

hours.

The continuous operation of the Rb frequency standards under laboratory conditions and over a long period of time at NBS has shown areas

where improvements were necessary and required. (The transistor circuitry replacement of vacuum tubes in the lamp exciter is one such instance. ) As further improvements are continuing, it is not difficult to

foresee failure-free, unattended operation of Rb standards for periods

greater than one year.

6. CONCLUSIONS

Over a period of almost four years these two particular rubidium frequency standards have given quite reliable service at NBS in performing

the many functions of continuously -running, transfer and reference standards. After initial malfunctions were corrected, largely through the use

of transistorized circuitry in the lamp exciter, improved operation resulted. For example, after such modification Rb-2 gave over 9000 hours

of trouble-free service from April 12, 1964, to April 17, 1965.

13
In terms of the USFS, lb-1 and Rb-2 each showed aging which aver13

ages to parts in 10 per day lor the periods under study. Assuming no

malfunctions, this indicates that if each frequency standard were left unadjusted, at the end of one year's continuous operation its frequency would

have changed only by parts in 10 . If the performance of Rb-64 during

a 3-month period is a good sample of the performance of improved models,

their aging would be considerably less. The day-to-day average stability

(standard error of estimate) of Rb-1 and Rb-2 advanced to about 0. 1 part

in 10 from the initial value of 0. 2 to 0. 3 parts in 10 . Further improvement is desirable in the general areas of aging and variability.

7. ACKNOWLEDGMENTS

We wish to thank Roger Beehler and his staff for the many calibrations

of the Rb standards in terms of the USFS, and Vincent Heaton, Catherine

Barclay, Joan Berube, Jean Petersen, and Ursula Palmer for their contribution to the data analysis work. We appreciate the help of Lyle Edlin

in various aspects of the data collection. Thanks are extended also to

Carole Craig for her careful typing of this paper.

14
8. REFERENCES

Andres, J. M. , D. J. Farmer, and G. T. Inouye (October 1959), Design

studies for a rubidium gas cell frequency standard, IRE Trans, on

MIL ELECT., MIL-3 , pp. 178-183.

Andrews, D. H. (December 1965), LF-VLF frequency and time services

of the National Bureau of Standards, Trans. Instr. and Meas. IEEE,

IM-14 , No. 4, pp. 233-Z37.

Arditi, M. , and T. R. Carver (January 1963), The principles of the

double resonance method applied to gas cell frequency standards,

Proc. IEEE, 51, pp. 190-202.

Barnes, J. A. (June 1964), Personal communication.

Barnes, J. A. , D. H. Andrews, and D. W. Allan (December 1965), The

NBS-A time scale - its generation and dissemination, Trans. Instr.

and Meas. IEEE, IM-14 , No. 4, pp. 228-232.

Barnes, J. A., and R. C. Mockler (September I960), The power spectrum and its importance in precise frequency measurement, IRE

Trans, on Instr. , 1-9 , pp. 149-155.

Beehler, R. E. , W. R. Atkinson, L. E. Heim, and C. S. Snider (December 1962), A comparison of direct and servo methods for utilizing

cesium beam resonators as frequency standards, IRE Trans, on Instr.,

1-11 , No. 3 and 4, pp. 231-238.

Beehler, R. E. , and D. J. Glaze (December 1965), Private communication.

15
Beehler, R. E. , D. Halford, R. Harrach, D. Allan, D. Glaze, C. Snider,

J. Barnes, R. Vessot, H. Peters, J. Vanier, L. Cutler, and L.

Bodily (February 1966), An inter comparison of atomic standards,

Proceedings Letters, Proc. IEEE, 54, No. 2, pp. 301-302.

Blair, B. E. , and A. H. Morgan (July 1965), Control of WWV and WWVH

standard frequency broadcasts by VLF and LF signals, Radio Sci. J.

Res. NBS 69D, No. 7, pp. 915-928.

Bender, P. L. , E. C. Beaty, and A. R. Chi (November 1958), Optical

87

detection of narrow Rb hyperfine absorption lines, Phys. Rev.

L. 1, No. 9, pp. 311-313.

Carpenter, R. J. , E. C. Beaty, P. L. Bender, S. Saito, and R. O. Stone

(September I960), A prototype rubidium vapor frequency standard,

IRE Trans, on Instr. , 1-9, pp. 132-135.

Carroll, J. M. (November 1962), Reliability: 1962, Electronics, 35, No.

48, pp. 53-76.

Crow, E. L. , F. A. Davis, and M. W. Maxfield (I960), Statistics manual

(Dover Publications, Inc., New York, N. Y. ), pp. 147-165.

Farmer, D. J. (May 1963), Performance and application of gas cell frequency standards, Proc. 17th Ann. Freq. Con. Sym. (U. S. Army

Res. and Dev. Lab., Ft. Monmouth, New Jersey), pp. 449-461.

Glaze, D. (April 1966), Personal communication.

Hudson, G. E. (August 1965), Of time and the atom, Physics Today,

pp. 34-38.

Kastler, A. (June 1957), Optical methods of atomic orientation and of

magnetic resonance, J. Opt. Soc. Am. , 47, pp. 460-465.

16
Lloyd, D. K., M. Lipow (1962), Reliability: management, methods and

mathematics (Prentice-Hall, Englewood Cliffs, New Jersey), pp.

190-195.

Looney, C. H. , Jr. (February 1961), A very low frequency synchronizing

system, Proc. IRE, 49, No. 2, pp. 448-452.

Mockler, R. C (May 1964), Atomic frequency and time standards, Radio

Sci. J. Res. NBS 68D, No. 5, pp. 523-527.

Mockler, R. C , R. E. Beehler, and C. S. Snider (September I960),

Atomic beam frequency standards, IRE Trans, on Instr. , 1-9, pp.

120-132.

Morgan, A. H. , and D. H. Andrews (April 1961), MSthodes et techniques

de controle des ondes kilometriques et myriametriques aux Boulder

Laboratories, Comit£ Consultatif pour la Definition de la Seconde

aupr^s du Comit^ International des Poids et Mesures, 2

6 session,

Annexe 6, (Gauthier-Villars & C

1S

, Paris), pp. 68-72.

Morgan, A. H. , E. L. Crow, and B. E. Blair (July 1965), International

comparison of atomic frequency standards via VLF radio signals,

Radio Sci. J. Res. NBS 69D, No. 7, pp. 905-914.

Natrella, M. G. (August 1963), Experimental statistics, NBS Handbook

91, Chapter 22 (Notes on statistical computations), pp. 22-1 to 22-4.

NBS (December 1964), World sets atomic definition of time, NBS Tech.

News Bull., 48, pp. 209-210.

Ostle, B. (1963), Statistics in research, (Iowa State University Press,

Ames, Iowa), 2nd Edition, pp. 159-206.

17
Packard, M. E. , and B. E. Swartz (December 1962), The optically pumped

rubidium vapor frequency standard, IRE Trans, on Instr. , I- 11, pp.

215-223.

Reder, F. H. (May 1963), Achievements and problem areas of atomic frequency control, Proc. 17th Ann. Freq. Con. Sym. (U. S. Army Res.

and Dev. Lab. , Ft. Monmouth, New Jersey), pp. 329-371.

Whitehorn, R. M. (May 1959), Gas cell frequency standards using buffer

gases and buffer walls, Proc. 13th Ann. Freq. Con. Sym. (U. S.

Army Res. and Dev. Lab. , Ft. Monmouth, New Jersey), pp. 648-654.

18
9. APPENDIX

9. 1. Description of Least Squares Statistical Program

for Use With High Speed Electronic Computer

The least squares program was written to obtain simple linear regression coefficients of standard frequency data which show an aging or

drift effect from day to day. This program analysis assumes an independent variable, y, corresponding to daily frequency values. The program

requires a set of data such as

X

l y i X

2 y 2

x., y., where j = 1 to n

and assumes a straight line as the best fit to these paired data. By the

method of least squares, one can determine the sample regression curve

of y on x by minimizing the sum of squares of the vertical (or y) deviations

of each frequency value from the average curve LCrow et al. , I960 J. The

equation of this sample regression line is y = a + bx, where a is the intercept and b is the slope of the regression line.

The program prints out both the input data (given in parts of 1 to

2 decimal places) and standard regression coefficients in summary form.

These regression coefficients are computed by formulas given in most statistical texts [see Crow et al. , I960; Ostle, 1 963 J. The program accepts

a maximum of up to 370 days of y frequency values. Missing y values are

neglected; however, the x values are advanced the corresponding number

of missing days; thus, each frequency value matches the day or x variable

it is reported for. Although the input data are given to 2 decimal places,

19
double precision techniques are employed in the program whereby 18

significant figures are carried in the calculations. The printout gives

half this number of figures, and the final results are rounded to be consistent with the original data. This follows standard statistical practice

to insure that errors of computation are small in relation to the statistical

quantity being determined LNatrella, 1 963 J.

20
OPTICAL PACKAGE

MODULATION

OSCILLATOR

107 HZ

PHASE MODULATOR

X 2 MULT

X2 MULTIPLIER

BUFFER AMPLIFIER

MICROWAVE CAVITY, LAMP ASSEMBLY

PHOTO CELL

T

10 MHz

10 MHz —

s/AR ACTOR

MULTIPLIER

X57

XI2 MULTIPLIER

6834 1| MHz

k

D.C. ERROR

CONTROL

5.000 MHZ

! CRYSTAL

OSCILLATOR

5 MHz

BUFFER AMPLIFIER

120 MHz

5 MHz

5^MHz

MIX

A "^MHz

i y

A 6 MHz

MIX +

V I MHz

BUFFER

AMPLIFIER

5 MHz I MHz

LOCKED OUTPUTS TO Rb TRANSITION FREQUENCY

BUFFER

AMPLIFIER

100 MHz

FIG. 1 BASIC SYSTEM OF Rb ATOMIC FREQUENCY STANDARD

21
AUGUST THROUGH DECEMBER 1961

CALIBRATION DATA NO CALIBRATIONS MADE

LIMITS SHOWN ARE ± 3 Sy/x

^1l|fYt^J I I l| I I I

1

1

Ll/f I, llf hMJL I

I I l| I I

I III I I I I

i r---._

PERIOD 1 PERIOD 2Q - /

Ku ll 1 I I ll I I 1 l| I I I llTTT-7-

7 14 21 28 4 II 18 25 2 9 16 23 30 6 13 20 27 4 II 18 25 AUG SEPT OCT NOV DEC

1961

JANUARY 1962 THROUGH JANUARY 1963

123

I I I I II I I I I I I II I II II I

I II I I

I I I I I I

I I I I I I I.I I M I I I I I

\PERIOD 3

PERIOD 4" ~"

i i i^rfiT^-ih i i i 1i i

i i| i i i i

|

i i i r|1~t^i|i M7"|n--i-Lj| ? i i i|i i i J I

! I|l !

I

1 1[ I I I |

I

I I l| I

I

I I |M I I |

I

I I l|| I I I |l I I I || I I I l|MJ_l I

I

I IJpl' I

I I Mil I I^Tl I I I II i I l| I I I l|l 1I IK I t I'M- I I Ml I I 1 II I I I III I I I I I I I II I I I i

7 14 21 28 4 II 18 25 3 10 17 24 31 7 14 21 28 5 12 19 28 2 9 16 23 30 7 14-21 28 II 18 24 I 8 15 23 29 6 13 19 27 3 10 17 24 I 8 15 22 29 5 12 19 26 JAN FEB MAR APR MAY JUNE JULY ~^ AUG SEPT OCT NOV DEC JAN

1962 1963

FEBRUARY THROUGH DECEMBER 1963

129

-130 —

6-131

1-129

Ld

<rLl

JH-uo

131

_ II 1 1

1 1

1 1 11 1 11 II 1 1 1 1 1 1

1 1 1 1

1 | II 1 l| 1 1 ! 1 || 1 || l| 1 1 1 l|l 1 1 L

—

PERIOD ioa

^PERIOD IOb ^\PERI0D 11

- 1 ^s* ^

PERIOD 12 H=

^*^^^_ ------ —

\ wv-»Yi<\ -. 1 1 1

1 1 1 1 1 1

1

1

1 M"fMJ ?l ' N^ 1

1 ll 1 1 1 1

1 11 i i|i i i ,-

1

I I ll

I

I I ill I

I

I II

I I ll II I III I

I

I

I

I II III I II ll II I llI I I Ijl II

oro/Ana - I PERIOD 12 __— —•— Rb-2

PERIOD 8 ^'Aj* s PERIOD 10 ^PERIODII

1

1 1 1 1

1

i

|

i i ~i~|Ti rif rrn"T~n~?~f~i i

7 14 21 28 6 13 20 27 3 10 17 24 I 8 15 22 29 5 12 19 26 3 10 17 24 31 7 14 21 28 4 1118 25 2 9 16 23 30 6 13 20 27 4 II 18 25 FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC 1963

FIG. 2 CALIBRATION DATA OF Rb-1 AND Rb-2

FROM AUGUST 1961 TO DECEMBER 1963

22
-123

-130

-129

-150

JANUARY THROUGH JUNE 1964

I 111111111111 I PERIOD PERIOD

I I I I I I I I I I I I I I I l I III

JANUARY 1964 THROUGH JANUARY 12, 1965

I

I I I I 1

I I I I I 1 I J

I I I II I I I I I I I I I TTT I M ii ii i i ii ii I I II I M l l l li I i I I I l I

i I i_ I

~E = DC 17a if^^VV^¥

I I I I I I I I I I I I I

IpERIOD

I l4

i I i i i 1 i i i i i 1 I I i i i PPr-i

I 15 31 15 29 15 31 15 30 15 31 15 30 15 31 15 31 15 30 15 31 15 30 15 31 15 JAN FEB MAR APR HAT JUNE JULY AUG SEPT OCT NOV DEC JAN 1964

-129

-130

JANUARY 13 THROUGH APRIL 16, 1965

I I I

I I

I I I I

I I PERIOD '

*-*Vi

I I I I I I I I I I I I I 1 I I

I 15 31 15 28 15 31 15 30 JAN FEB MAR APR 1965

• . CALIBRATION DATA NO CALIBRATION MADE

LIMITS SHOWN ARE ±3Sy/„

THE FOLLOWING MEASUREMENTS ARE IN TERMS OF 24 HR DCO VALUES:

a. ALL 1964 Rt DATA

b. Rb-64 DATA FROM FEB. 13 -APR. 8, 1964

C. Rd-2 DATA FROM APR.I2-NOV. 27, 1964 ALL OTHER MEASUREMENTS ARE USFS POINT VALUES

FIG. 3 CALIBRATION DATA OF Rb-1 AND Rb-2

DURING 1964 TO EARLY 1965

(Rb-64 DATA GIVEN IN PERIOD 13)

23
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1-

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UJ>O5

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UJ5* o ur UJ CO <? tr Li- (T < C\J ce UJ

<t 5

00

L£p Q_

UJ

?• >- < _l Q

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UJ 1 1 1 Lt o n O < X X ) (0 01 en o CO CO o 0)

c/) o O o o ro h II II II II II co

<r ^

UJ 2

_i >*

O

U_ CO

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u_ < o T' H O-l

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r- UJ UJ Ha:

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LO LJ_J

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D

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u_

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a-j :__, Ll

X

=? !—

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Lx-l >

hLO

-^ <

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u.

LOI

01 01 Nl 'Sid -A3N3nt)3aj 1VNIIAJ0N

25
>-

3

O

UJ

or

Ll

u

Z

UJ

a.

CO

LL

Llo

_)<

-12?

-128

-129

130 o

O

2!

CO

h0_

| CO

Li_ LU CO 2 ~) UJ

crUJ

Li_ u. O UJ

cr CO ci > i- or

co

I

I

I

I I TT I I

I

I NOTE:

I. ARROWS INDICATE WHERE ADJUSTMENTS WERE REMOVED.

2. LIMITS SHOWN ARE ± 3 Sy/

I

I

I I I

1

I

I I II II I

I

I I I I

I

Rb-2 —RUBIDIUM

NOMINAL OFFSET

-74

-75

re

A-218 - CESIUM

U

UJ

cr

hi

U.UJ

cr

i-UJ

CO

u.u.o

_l<

130

132

STATISTICS

(PTS.IN IO HO )

FREQUENCY STDS. Rb-2 A-218 Rb-i

n (DAYS) 96 96 84

b (PER DAY) +0.008 -0.002 -0.006

Sy (STD. DEV.) 0.53 0.18 0.35

Sy/X (STD. ERR. EST.) 0.2l 0.13 0.12

y (MEAN) -129.10 -74.73 -130.99

r (COEF. CORRELATION) + 0.92 -0.65 -0.94

NOMINAL OFFSET

-

] Rb-1 -RUBIDIUM

II

15 31 15 30 15 AUG SEPT OCT 196215 30 15 NOV OEC

l|

15 31 15 28 JAN FEB 1963

FIG. 6 FREQUENCY COMPARISONS OF Rb AND Cs ATOMIC FREQUENCY

STANDARDS FOR 6 MONTH PERIOD. (TERMS OF USFS)

26
J>N .fit*

OJI

orQ<I -Q

in oc

Ndu«

OJ

»~_ ExEi

a. d.

10

r- o

ii o

CVJi rj ;n c/) IX CM UJ

—i

O 1 Z

_j >

cr 1

cr

C/3 UJ

h- l ID Z

<!

UJ

cr

«3 z

IT

X 3 c

f—

O E 2 or ui

cd UJ

UJ

fliJ

UJ$O

V-<

_l UJ

m o

_J z

UJ

UJ5 O

1-3 < X O hcr. oo

in

<5 Cfl CD hUJO O z Z z

UJ LO o

cr

H

UJ

Llu_

cr

<!

cr

Q

Q > —*

C/5 h-D

CLh-DONI

-*: oooogoo

27
-O

CMI -Q

orl

-Q

cr

>-q:o

i-coI

UJo>

orUJCO

oo

sanoH - jaiw

28
TABLE 1 SUMMARY STATISTICS OF Rb STANDARDS FREQUENCY DATA

PERIOD

Rb - 1 STATISTICS Rb - 2 STATISTICS

n b S

b S

y y/x y r a n b S

b s

y y/x y

r a

1 a + 0.021 0.006 0.31 0.24 -129.42 0.64 -129.74 22 + 0.031 0.007 0.43 0.32 -129.93 0.69 -130.42

<£> 2 56 -0.012 0.001 0.45 0.23 -129.81 -0.86 -129.17

0) 2a 32 -0.010 0.002 0.23 0.17 -129.70 -0.66 -129.44 2b 36 -0.005 0.001 0.18 0.16 -130.27 -0.49 -130.10

3 32 -0.021 0.001 0.34 0.13 -130.41 -0 93 -129.8? 3a 13 -0.022 0.003 0.15 0.07 - 130.29 -0.90 -130.07

<\J 3b 25 -0.020 0.002 27 0.11 -130 2/ -0 91 -129 88

<y> 4 53 -0.004 <0.00l 0.17 0.15 -129.91 -0.54 -129.73 56 -0.003 0.001 0.15 0.14 -130.09 -0.41 -129.98 5 38 -0.006 0.001 0.14 0.10 -130.39 -0.70 -130.21 38 -0.014 0.002 0.33 0.21 -130.37 -0 78 -129.91 6 44 -0.007 <0.00l 0.19 0.12 -130.41 -0.79 -130.17 62 +0.005 < 0.001 0.22 16 -129.58 0.71 -129.83

73 -0004 < 0.001 0.15 007 -129.79 -0.89 -129.56 48 +0.016 0.001 0.38 ..16 -129.28 0.91 -129 32 8 X 22 +0.006 0.002 09 07 -130.29 0.66 -130 40 9 * 20 +0.018 0002 1? 0.07 -,29 85 0.91 -130.16

rO

ID 10 72 -0.0002 < 0.001 0.13 0.13 -130.31 -0.06 -130.30

Ol 10 a 20 -0.010 0003 0.13 09 -129.91 -0.69 -129.75 10b 26 -0012 0001 0.21 0.07 -130 49 -094 -130.21

1 1 32 -0.017 001 0.26 0.09 -130.44 -0.94 -130.00 26 -0.010 < 0.001 0.13 0.05 -130.24 -0.91 -130.05

12 14 -0.004 0.004 09 0.09 -130.12 -0.25 -130 08 54 +0.004 < 001 0.13 0.10 -129 96 0.65 -130.10 13a * mr^#/yA^//y& 0.96 W/,/yiyWd 13b 17 -0 036 0.003 0.19 0.06 -130.14 -0.95 -129.82 m'4¥//w//tyyy-K^MMW//

13c 14 -0016 0.006 0.10 008 -129.79 -0.63 -129.68

10 13d 15 -0.010 0.005 0.09 009 -130.26 -0.46 -130 19 o> 14 17 +0.011 003 0.07 005 DC. 37 0.74 -130.47 13 -0.018 0.002 07 0.02 -130.17 -0.95 -130.04

15 40 -0.028 0.001 0.34 0.09 -130.37 -0.97 -129.80 100 -0.010 <0.00l 031 0.06 -13042 -0 98 -129.89

16 * 98 -0 008 <0.00l 0.25 0.07 -130.30 -0.96 -129.88 17a * 17 -0.007 005 0.11 0.11 -130.10 -0.33 -130.03 17b * 30 -0 1

1

<000l. 0.16 04 -150 43 -0.97 -130.18 m 18 * II -0 004 0003 0.04 004 -i29 a -0.50 -129.69

01 19 * 45 -0.004 <0.00l 09 0.06 -130.20 -0.77 -130.08 20 K 12 -0.025 0.003 0.13 0.05 -129.85 -0.92 -129.63

STATIST

n =

b = s b

=

Sy/x =

y

ra***

ICS NOTATION (DATA GIVEN IN PTS. IN 10 — 1961, 1964 AND 1965 DATA ADJUSTED

TO NOMINAL OFFSET OF -130.00 X IO~ 10

) NUMBER DAILY REPORTED CALIBRATIONS

SLOPE OF LEAST SQUARES LINE THRU DATA (DRIFT PER DAY)

STANDARD DEVIATION OF SLOPE STANDARD DEVIATION OF DAILY VALUES ( INCLUDING SLOPE CONTRI BUTION ) STANDARD ERROR OF ESTIMATE ( VARIATION ABOUT LEAST SQUARES LINE) AVERAGE DAILY VALUE

^COEFFICIENT OF CORRELATION

INTERCEPT OF LEAST SQUARES LINE OUT OF SERVICE FOR MODIFICATION

Rb -64 DATA - (Rb-2 IN REPAIR )

29
CM

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CM CM CM o 00 00 o O o 1—1 o o o O o o o o £1 • o o O o o o o + 1 + I 1 1 o CM <* 00 00 CM S o "^ o Lfl ^o lO

CM i—

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CM

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CM o o OO lO

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X> CO

O o O o o

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ro h- CM o o o o i—I 1—1

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XI o o o o . o o1 o1 o o o1

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31 GPO 858- 646


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