Table 1. Summary of typical frequency response measurement uncertainties for photodiode
with rf power sensor and 3 dB attenuator.

Source of uncertainty Uncertainty,
k=1,%
Type A
Measurement repeatability s <0.05
Offset correction s, 0.007
Environment effects s, (fin GHz) 0.106 + 0.00064 f+
0.00024 f?
Type B
Meter range scaling 0.5
Meter offset 0.023
Optical power drift (power matching) 0.06
Bias current measurement 0.08
Power sensor noise, @ 0.05 GHz 0.025
@-3 dB point 0.05
Total uncertainty (rss), @ 0.05 GHz 0.52
@ -3 GB point, 31 GHz, 4 scans 0.63
Expanded uncertainty (coverage factor k = 2), @ 0.05 GHz 1.05 (0.05 dB)
@ -3 dB point, 31 GHz, 4 scans 1.25 (0.05 dB)

of four scans over each range. The response and its standard uncertainty at the requested
frequencies are found using the following method. Let R?(f) be the measured response at
frequency f. The calculation is usually performed withR’(f) in dB with negligible error because
the scatter in the data is small. The response at the requested frequency x is estimated by a
kernel-type smoother [17]. Specifically,

~ » (5 <Aleu)
R? (x) = Hib) ; (9)
¥4

el

14


Appendix B: Heterodyne system with unequal powers

The powers from each laser incident on the detector may not be equal. In this case it is possible
to formulate the expression for the normalized response in a way that eliminates error from the
assumption that the powers are equal used in eq (6). But first it is illustrative to calculate the
error induced by small deviations from equality. Let the optical powers be nearly equal, so that
Po, = Po and Po) = Po +6, where 5 « Po. Then

(Po + Poy = APS + Pf) + &, (Bl)

2(Po;Po2) = AP + Pod)

“He ‘or + Pon) - @)

The last two lines of eq (6) then follow from eqs (B1) and (B2). The error caused by a small
perturbation can then be approximated as

2P, <p,
<ij>R,  0.5<i5>R,
_ __ WPoPodR*)
0.5(Po, + Po;R7(0)
UP, + OP
~ Co * Mo 924)

0.5(2P, + 6)

[: + 4]
P,
wp 2h
ie
2P5
; 42) . -]
4 Po

35

(B3)

=P)



power sensor are permanently attached and the combined normalized response is further
normalized to give 0 dB at 50 MHz.

In the case of the receiver without access to bias current (see Appendix D), the modulation depth
of an unknown source can be found in terms of the measured rf power, average optical power,
and known voltage frequency response as

2R,P.
Mo =. (6)
G ‘avg

A.2 Calibration transfer using ratio of measurements

The fundamental problem in making photodetector frequency response measurements is getting
accurate knowledge of the modulation depth of the source. The modulation depth of the
heterodyne beat signal is known from fundamental principles, but the modulation depth of a
directly modulated laser diode is not. The modulation depth of a Mach-Zehnder modulator can be
measured, but careful control of bias and net optical transmission are required for accurate
measurements. A transfer standard calibrated using the heterodyne techniques described above
and the ratio measurement system shown in figure Al can be used to obtain accurate knowledge
of the modulation depth of these sources. The ratio system consists of a modulated light source
with unknown modulation depth and a 1 x 2 coupler. The coupling ratio does not need to be
specified. The signal from the coupler is delivered to a DUT and to a reference photodiode
attached to a rf power sensor. The modulation depth of the source can be calculated using eq
(35) and the known frequency response of the transfer standard photodiode. Then the frequency
response of the DUT is

Pepur

Rou) = | (A?)

1
MG 0.5<igepur?Ry

Calculation of the DUT’s frequency response this way includes calibration uncertainty of both the
power sensors used to measure P ,, from the standard detector at NIST and at the customer’s
laboratory, giving a total expanded uncertainty of 0.2 dB or more for the modulation transfer
function. Combined with other factory uncertainties, this may give an unacceptable uncertainty
for the intended test system.

One possible alternative is to calibrate the response of the photodiode combined with the rf power
sensor. This method totally eliminates uncertainties due to power sensor calibration and
impedance mismatch. When the photodiode/power sensor combination transfer standard is used

in the ratio test system, the combined frequency response is used to find the modulation depth of
the source

31


Appendix E. Sample calibration certificate

U.S. DEPARTMENT OF COMMERCE
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
ELECTRONICS AND ELECTRICAL ENGINEERING LABORATORY
Boulder, Colorado 80303

REPORT OF CALIBRATION

Reference Receiver
XXX photodiode, Serial No. xxxxxxx
XXX power sensor, Serial No. XXXXXXXXX
XXX 3 dB attenuator, Serial No. xxxxxx

Submitted by:
Manufacturer’s Name
Street Address
City, State Zip

The combined normalized frequency response of the Reference Receiver was measured at 1.319
uum. The Reference Receiver consists of a photodiode with bias current monitor circuit, a 3 dB
attenuator or bias tee, and an rf power sensor. Measurements were made in the following
frequency bands:

200 - 900 kHz, 100 kHz steps

1 - 40 MHz, 0.5 MHz steps

41 - 119 MHz, 1 MHz steps

120 - 600 MHz, 3 MHz steps

630 - 4200 MHz, 15 MHz steps
4250 - 40000 MHz, 50 MHz steps
40100 - 50000 MHz, 100 MHz steps

MAWRYENEO

Since the power sensors are fixed they can not be refered to the 50 MHz reference oscillator on
the power meter. Hence the “combined normalized response” R?(f) was further normalized to 1
(0 dB) at 50 MHz. Bands were spliced together with offset corrections typically on the order of
0.01 dB or less. The typical uncertainty in the measurement results is less than +0.05 dB
(coverage factor k = 2) below 36 GHz and is dominated by uncertainties in the power meter.

Page: Page x ofy
Calibration No.: XXXXX
Date of Report: month xx, 199x 40


Optical Input
; Per Lasers

1GHz
3.dB Fiber Amplified
Coupler Receiver 5 GHz Amplifier
——}€-4 input 2
2s 92(f) - 2.4(m) Counter
Pp>—>—H4 Input 1
40 GHz 2.4(m) - 3.54
Detector 50 GHz 24 300

Amplifier

Figure 3. Frequency counter subassembly for operation below 40 GHz. Although input 1 is
specified between 500 MHz and 40 GHz, it does operate, with some cut-outs, below
500 MHz. Input 2 operates between 10 Hz and 80 MHz in high Z (1 MQ) mode and
between 10 MHz and 525 MHz in 50 Q mode. The 3 dB coupler can be omitted and
the optical input can go directly into the high bandwidth detector for high bandwidth
scans where the detector sensitivity is degraded.

present, the highest resolution achievable in swept mode is about 300 kHz, although the
resolution may be considerably worse when the frequency is swept quickly (for example when a
much larger data spacing is desired). Higher resolution can be achieved using the phase-locked
loop described later in this chapter. Since the frequency range of the rf counter is limited to
about 40 GHz, an external mixer is required to down-convert frequencies above 40 GHz to a
range where the counter operates. The circuit for down-conversion of frequencies in the 40 to
55 GHz range is shown in figure 4. The beat signal is generated in a 40 GHz bandwidth detector
and amplified in a 50 GHz bandwidth amplifier. This signal then enters the rf port of the mixer.
The LO (local oscillator) is provided by a Gunn oscillator operating at about 62.15 GHz. The

down-converted signal from the IF port is then amplified with a 26 GHz bandwidth amplifier and
fed into channel 1 of the rf counter.


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relatively large uncertainty, while the shape is specified with much lower uncertainty. The
technique described below is valid for logarithmic data if the offsets or outliers are less than a
few tenths of a decibel; otherwise, the calculation should be performed with responsivity in linear
units. If this were the case, the procedure below would need to be modified to accommodate a
linear scale factor instead of a shift.

If there are m scans over m overlapping frequencies f,, then offsct adjustment factors can be
calculated by minimizing the expression

Las ~ 4, VF) - ay ~ >» Un(Fi) — Im) » (19)

where d(- ,-,-, +) is an "appropriate" distance metric and ¥,,=10log(R’, ) or 10log(g7 ), as
appropriate for the particular measurement (see Appendices A and D for definition of g). A
possible metric for our application is absolute deviation from the mean. Let

Wf) = > 4)

jl om

(20)

be the mean response at f, and define the distance metric as the sum of the distance (absolute
difference) between AGA) - 4, and the mean response (fj)

ANA) ~ ap ~ > TA) ~ 4) = DNA) - a - YA - (21)

Fl

The expression we need to minimize is

m

LV WA - 4 - WHI - (22)

Fl #1

Given the sequence y,, y2, ..., ¥p the value of a that minimizes

k
y ly,-al (23)

is a= median of y,, y,, ..., y;- Thus the solution for a, is that a; is the median of
YHA) - Wh) YA) - Wh) “> Vf.) ~ Wf,,) : (24)

18


Hence, a 4 % fluctuation in Po, will cause a 12

0.04 % or 0.0017 dB change in the measured

value of 8(/). 4

On the other hand, large differences between x a]

the laser powers can lead to large errors in eq o

(6), even if the individual photocurrents are 3

known. This error is shown in figure B1. © 7

This problem can be overcome by monitoring 5

the individual photocurrents and using the Ai 4

exact ratio

P.
Wf) = —L. BA
2i,1,R, (84) Os ot
~50 -25 tt) 25 50
1008/Po, %
Figure B1. Error in ratio if total current is used
instead of product of individual

currents in eq (6).

Appendix C: The meaning of normalized response and 0 dB

A simple interpretation of the normalized response is the ratio of the rf responsivity (refered to the
output (rf) port) to the de responsivity (refered to the bias (dc) port). A normalized response of 0
dB then can be interpreted as the de and rf responsivities (as defined in eq (4)) being equal. Since
the rf responsivity is refered to the output port, the effect of any attenuators in the output path
will be shown as an offset. For example, a detector followed by a 6 dB matching pad will show a
normalized response that approaches -6 dB at low frequencies.

Another interpretation for 0 dB is that the rf signal from the photodiode is the maximum possible
without driving it into forward conduction. That is, if the de current is i, then the rf current has a
maximum of +2i, and a minimum of 0.

The normalized response may be greater than 0 dB in steady state operation when the detector

has some gain or the detector includes some inductive resonance. In the latter case, the diode
current source drives an LRC tank circuit.

36


Contents

1. Introduction............... SS 1
2. Principle of heterodyne frequency response measurements ...........0.. cee cee eee eens 2
2.1 Photodiode with access to bias monitor 3
2.2 Combined photodiode/rf power sensor transfer standard ............... eee eee 5
3. Nd:YAG heterodyne measurement system ........ 60.60 eee eee eee tenet ence eens 6
3.1 Basic setup and swept operation .
3.2 Phase-locked operation ......... 0... c cece cee cece eee eee eee eens
3.3 Power matching ........ cece cee eee cece ee eee een eee een eens
4. Uncertainty in combined photodiodc/power sensor normalized response ...........5055 13
4.1 Type A uncertainties 20... 0. cece cece cee ence eee e ne enes 13
Repeatability... 0... cece ccc cence cece nent e tence snes 13
Offset correction .. 17
Environmental conditions .19
4.2 Type B uncertainties....... .24
Meter range scaling . 24
Meter offset .............0086 +24
Optical power drift (power matching) 24
Bias current measurement ......... 24
Power sensor noise ........ 24
Reference power uncertainty .. ..25
Gunn oscillator frequency drift .
Hysteresis . .
Relative intensity noise
5. Quality Control 2.0... cece cece eee ene e eee n teen een eee eens
5.1 Calibration notebook 2.6.00... 6. eee eee nent ence ees
5.2 Checks on each calibration
5.3 Periodic checks ..........
Power stability ©... 0... c ccc cece cece eee ener nen e eens os
Gunn oscillator frequency... 0.6... cece eee eee eens 26
Check standards ........ ..26
5.4 Future system changes .............. 0 eee eee ..27
5.5 Transfer standards which are suitable for calibration .............0.00e0ee eae 27
6. References... cece eee nen eee nen beeen tent ee 27


18. Hadle, W. Smoothing techniques with implementation in statistics. New York: Springer-
Verlag, 1991.

19, Altman, N. S. An introduction to kernel and nearest-neighbor nonparametric regression. Am.
Statistician, vol. 46, pp. 175-185; 1992.

20. Rice, J. Bandwidth choice for nonparametric regression. Amn. Statistics, vol. 12, pp. 1215-
1230; 1984.

21. Mood, A. M.; Graybill, F. A.; Boes, D. C. Intoduction to the theory of statistics. New York:
McGraw-Hill; p. 257; 1974.

29


where b is the bandwidth parameter and K(-) is the kernel function, which typically has the
following properties:

1. KE) = 0 for all &
2. f "KEE = 1 (10)

3. K(-8) = K(@) forall &

That is, R? (x) is obtained as a weighted average of frequency responses around x. The kernel

function assigns the weight to each point, and the bandwidth b determines the size of the region
around x for which R?( J;) receives relatively large weights. Frequently used kernels include
rectangle, triangle, and Gaussian functions. The rectangular kernel assigns equal weight to the
points inside the rectangle and ignores the points outside. Both the triangle and Gaussian kernel
assign the most weight to the points that are closer to x. In our applications, we use the
Gaussian kernel

-2
K@) = —1~ ¢ 2037 | (11)
0.37/20

The kernel is scaled to have 25th percentile of -0.25 and a 75th percentile of 0.25.

Many methods have been proposed for bandwidth selection.[18] In practice, b can be
determined by the average frequency increment in the scan, and the desired number of points

used to calculate R? (x). For example, if the Gaussian kernel is used, the average frequency

increment is h, and roughly p points on each side of x arc to be included; that is,|x - f| < ph.
Any point with |(x - f)/b| > 1 receives almost 0 weight; that is, we want |(x - f)/b| < 1 or
b = ph. The “resolution” of the measurement is then about 0.37ph. We typically take data so
that the spacing between acquired points is 0.1 to 0.2 times the final data spacing (resolution)
required. We then use p = 2 giving an approximate resolution of 0.07 to 0.14 times the
customer’s requested frequency spacing.

The kernel-smoothing technique, like all other smoothing techniques, has an error associated
with it. This error is small when the response is roughly linear with frequency, but may become
significant in regions with large curvature. The approximate mean-squared error of the kernel

~
estimator R? (x) is given by [19]

15


oma 7125/97
© 0.08 —————— 11/20/97
a] ———— 1/8/98

-0.08 | T T T T T

t) 20 40 60
Frequency, GHz

ft) 20 40 60
Frequency, GHz

Figure 9. Measurements on highband of the check standard. Top graph shows deviation from the
mean which neglects measurements on July 25, 1997. Bottom graph shows the 20
variation with a fit to a quadratic equation. Spikes at 52 GHz go out of the range of the graphs.

21


2
&

is the between-scan uncertainty and Fs J
o
sa) - p SO 5 -92-| .
fm as) 3 Pra |
3 :
= 967
is the uncertainty within a scan due tokernel 2
smoothing. Repeatability is a function ofthe 8
rf connector type, frequency, electrical 3
mismatch, and other factors that cannot be “9-10.07
controlled. E J
z
Other smoothing techniques can also be used, 10.4 7 T r T r T r
in particular, spline methods. We did not use 22.5 23.0 23.5 24.0 24.5
a spline method to interpolate the . Frequency. GHz
measurements because spline methods give Figure 7. Dots represent the measured response,
unsatisfactory results near the end points, use 4 denotes the interpolated responses at
arbitrary knot spacing, and give a poorly requested frequencies based on a cubic
defined resolution. In addition, the splines spline fit, and x denotes the Gaussian
over-smooth the peaks and valleys. For kernel smoother.

example, the dots in figure 7 represent the

measured response, 0 denotes the interpolated responses at requested frequencies based on a
cubic spline fit, and x denotes the interpolated responses at requested frequencies based on the
Gaussian kernel smoother. In most cases, both methods agree well, but clearly the spline method
gives poorer results in the neighborhood of 23.5 GHz. Uncertainty due to the kernel smoothing
is negligible on most detectors that we have calibrated; for example, s, < 0.002 dB for the data in
figure 6.

Offset correction: When the power sensor gain is not scaled to the 50 MHz power reference (or
when the frequency response is normalized to the optical power instead of the photocurrent), a
correction due to the scale factor must be included. The scale factor (offset on a logarithmic
scale) is constant for each scan and does not have a frequency dependence if coherent multipath
effects are insignificant. The fiber connector insertion loss repeatability is typically about 0.1 dB
and is larger than other uncertainties in the measurement. Variation in the scale factor is
normally about 0.005 dB. However, if the meter is used with a different power sensor and it is
scaled relative to the 50 MHz reference, the scale factor could change by a few tenths of a
decibel. Also, scans over the low and high frequency ranges are often made separately and with
different data spacing, so a method for "splicing" the two overlapping frequency ranges is
required. This is accomplished by shifting all the scans to a common level (on a logarithmic
scale) selected by a least-median technique. Using this technique, the individual scans are shifted
by averaging over all desired frequencies where scans overlap. The entire data set is then
normalized to give 0 dB at some frequency, typically 50 MHz. The absolute response then has a

17


Appendix A: Use of transfer standard in a ratio system
A.1 Application of heterodyne formalism to arbitrary modulation depth

Signals that do not have 100 % modulation depth are commonly used in optoelectronic test
equipment. An arbitrary modulation depth can be synthesized by varying one or both of the laser
powers in the heterodyne system and can be modeled using the same formalism as section 2.1
above. The resulting equations are applicable to any source with an arbitrary modulation depth,
such as a laser with direct or external modulation. A notationally simple way to change the model
is to let P,,, denote the total average optical power incident on the detector, Po, = @Py,, and Po,
= (1 - @)P,,,. Then the total optical signal incident on the photodiode is

P()= Pag * 2PaygV (1 — @) cos(2mft) . (Al)

The average optical power is then P,,, and the absolute modulation depth is 4P,,,/@(1 - a)]* , or,
in fractional units, the fractional modulation depth Mo is

Py
Mo = ay = 2Va(l - a), (A2)
avg

where P,,,, and P,,, are the maximum and minimum optical powers incident on the receiver. The
mean squared currents in the photodiode are

<igg > =Pang R70) (A3)
and
SUZ? =2P yg (1 - a)R*(w) , (A4)
so the ratio of the powers is
2P
= MSR). (a5)
Sig7R,

Hence, the modulation depth of an arbitrary source can be measured with a detector of known
normalized response. The combined normalized response can be used in eq (AS) if P,, is used
instead of P,, Ifthe normalized response is only known to within a constant scale factor, the
modulation depth is known only within a scale factor. This is the case if the photodetector and rf

30


ECL TTL crystal
comparator oscillator
RF 60 MHz
Low-pass 55 MHz
Filter
Mixer
ECL phase/frequency
detector o pte
R2
Low-pass
C1 R3 Filter
to piezo and
thermal controls| RI

1 |
4 Loop filter

Manual gain
adjust

Figure 6. Schematic of PLL box from figure 5. Component values for the loop filter are RI=137
Q, R2= 158 kQ, R3= 3 Q, and C1= 1 pF.

3.3 Power matching

The NIST heterodyne system is designed to operate with 100 % modulation depth and to use the
normalization described by eq (6). Control of the modulation depth is achieved by three features
of the system: mode matching of the radiation incident on the detector from each laser,
polarization matching, and power matching. Mode matching is achieved by launching the laser
beams into roughly 2 m of single mode fiber. Polarization matching is provided by the polarizing
isolators. Any birefringence in the optical path following the isolators changes the relative
polarization of the two laser signals by a negligible amount. The power from each laser is
matched by fine adjustments of variable beam splitters VBS1 and VBS2. Typically, a high power
is required for the high speed detector used for frequency measurement, so the ratio of the power

12


work phase can be neglected. Equation (4) assumes that the detector is reverse-biased and uses
the convention of positive current flowing in the reverse direction of the diode. The first term on
the right side is the de photocurrent, which flows through the bias supply, and the second term is
the rf photocurrent, which flows through the rf load (the microwave power sensor) through a de
blocking capacitor. The mean squared photocurrent generated by the photodiode is

<ig(f)> = (Poy + Pon)? R20) + 2Poy Pop RUA) 6
= <i> + <i> ‘
If Po, is nearly equal to Po, then 2(Po,P,,) is, to first order, equal to 0.5(Py, + Py,)*, as
discussed in Appendix B. The normalized frequency response 8?( f) which is defined as
R°( f /R°(0), can then be found by taking the ratio of the rf electrical power P,, to half the de
electrical power delivered to a load R, ,
32
2P iy _ <i R,
<ig2>R,  0.5<i3,>R,
. Po PopR 2—)R, L 05)
0.5(Po, + Po,?R(O)R,
a~RWY .
R(0)

P,,is a function of frequency. It includes corrections for the sensor calibration factor and
electrical mismatch, and is the power that would be delivered to an ideal load R, [9].
Measurements are typically made with transmission lines and loads with characteristic impedance
of 50 Q; however these equations also apply to measurements with 75 Q systems. The
normalized frequency response may be quoted in decibels as 20log[R(f)]. All NIST calibrations
report the normalized response in 20log[#(f)] format. The electrical bandwidth of the device
is where 20log[R(f)] falls by 3 dB from the low frequency level [3].

In an ideal measurement <i,,?> is constant, but in any real measurement system it may vary
because of changing optical power coupled to the photodiode. The ratio in eq (6) is insensitive
to optical power variations. Using the normalized response also simplifies the measurement
apparatus because only the total photocurrent in the photodiode need be monitored instead of the
power coupled to the detector from each laser.

The normalized frequency response is an unbiased method for comparing measurements made
with different systems. A common practice when comparing frequency response measurements
is to add an offset to each curve to make the responses equal at some frequency or over some


standard itself. As further measurements on the check standard are acquired, the estimate of s,
will be modified.

5.4 Future system changes

Possible future system changes could include, but are not limited to, replacement of YAG2,
modification of YAG3, use of an electrical spectrum analyzer for frequency measurement, use of
an additional laser for extending the frequency range above 60 GHz, replacement of the 40 GHz
bandwidth detector, or corrections for system “bugs.” Future system changes will be
documented in a calibrations notebook which will be kept with the system. Instructions which
are specific to the NIST heterodyne system and data analysis are also kept with the system.

5.5 Transfer standards which are suitable for calibration

The transfer standards must include a connectorized single-mode input fiber. The fiber
connector should be clean and scratch free. The photodiode response should be free of sharp
features to minimize calibration uncertainty. The photodiode must have either direct access to
the bias point or have an internal current monitor circuit which is stable so that correct
normalization can be achieved during each measurement scan. Coaxial rf connectors must be of
a precision type, free of debris and in good condition. The power sensor must mate with a
power meter which can be controlled via a standard GPIB interface. Depending on the make and
model of the power meter used, the customer may be asked to include the power meter with the
transfer standard for calibration. Transfer standards which are determined by NIST to not meet
these requirements will be returned at the customers expense and will be charged for any labor
which may have been required at NIST to determine the suitability of the transfer standard.

6. References

1. Optical interfaces for equipments and systems relating to the synchronous digital hierarchy.
CCITT (now ITU-TS) recommendation G.957, Geneva; 1990.

2. In this work, all ratios are stated in decibels electrical, that is, 20log(A,/A,) where A is a
voltage or current. Absolute powers are stated with the reference level, such as - 10 dB (re: 1
mW) instead of - 10 dBm as suggested in Letter symbols to be used in electrical technology,
Part 3: Logarithmic quantities and units, TEC 27-3, Geneva; 1989.

3. Valdmanis, J. A.; Rudd, J. V. High-speed optical signals demand quick response. Laser
Focus World, pp. 141-147; Mar. 1995.

4. Humphreys, D. A.; Lynch, T.; Wake, D.; Parker, D.; Park, C. A.; Kawanishi, S.; McClendon,
M.; Hernday, P.; Schlafer, J.; Gnauck, A. H.; Raybon, G.; Hawkins, R. T.; Jones, M. D.; Goll,
J. H. Summary of results from an international high-speed photodiode bandwidth
measurement intercomparison. Digest, Optical Fibre Measurements Conference, York,
U.K., pp. 69-72; 1991.

27


s,= [e242 as? @9)

as the total type A uncertainty in Table 1, s’ is obtained using the offset adjusted data in eq (16),
mis the number of scans within the particular frequency band, and s,” is the maximum of the 5a)
(see eq (27)) for all the scans and frequency bands. If offsets are not required s, =

4.2 Type B uncertainties

Meter range scaling: This uncertainty is due to the inaccuracy of the gain for different power
ranges. The absolute accuracy of the power meter is specified by the manufacturer as 0.5 % and
is assumed to be 10. This is conservative; if the specified uncertainty were actually 20 the
estimated calibration uncertainty would be reduced. Also, the uncertainty is assumed to obey a
Gaussian distribution instead of rectangular distribution. This is also a conservative assumption.

The meter range scaling uncertainty is the dominant contribution to the uncertainty budget in
Table 1.

Meter offset: The settability of the zero level, specified as one least significant count on the
display or 0.001 dB (0.023 %), is assumed to be 10. Additional zero setting error is 0.5 % of
full scale deviation of lowest range. For the diode power sensor this is 5 pW.

Optical power drift (power matching): Power from one or both of the lasers that is coupled into
the fiber may drift during the measurement. Also because of the long coherence length of the
Nd:YAG laser, multipath effects cause the power matching between the two lasers to vary with
frequency. The power from each laser does not drift by more than 4 %, giving a 0.04 %
uncertainty in the ratio of eq (6). This quantity isassumed to be 10 for one of the lasers. Adding
the uncertainty in quadrature for two lasers gives +0.06 % uncertainty.

Bias current measurement: The scale factor in the current monitor used in the check standard
has a temperature coefficient of about 0.14 %/°C. Using the laboratory drift of about +0.28 °C,
the uncertainty in the bias current is 0.04 %. Squaring gives a 0.08 % uncertainty in the
normalized response. If a bias current monitor is not provided, the voltage drop across a 1 kQ
resistor in series with the detector is measured. The temperature coeflicient of the resistor is
0.01 %/°C giving 0.0028 % uncertainty. The specified accuracy of the voltmeter on the 300 mV
range is 0.0025 %, which is assumed to be 10. Other current monitor circuits may have different
uncertainties. The dark current and/or offset of the monitor circuit is subtracted from the
measured current.

Power sensor noise: This is the uncertainty associated with the background noise of the
detector, which is about -75 dB (re: 1 mW) for the diode power sensor. Using 100 pA total

24


Calibration Service of Optoelectronic Frequency Response at 1319 nm for
Combined Photodiode/rf Power Sensor Transfer Standards

Paul D. Hale and C. M. Wang

National Institute of Standards and Technology
Boulder, Colorado 80303

This document describes the Calibration Service provided by the National Institute
of Standards and Technology (NIST) for optoelectronic frequency response
transfer standards and their use in measuring optical modulation depth. The
service supports the calibration of transfer standards consisting of a pigtailed
photodiode, with access to the bias current, combined with an rf power sensor
over the frequency range of 300 kHz to 55 GHz at 1319 nm. Typical
measurement uncertainties are about 0.05 dB, which includes measurement
repeatability, rf power meter scaling accuracy and offset, optical power drift, bias
current measurement, and power sensor noise. The measurement technique, based
on the heterodyne beat note between two single-frequency Nd:YAG lasers
operating at 1319 nm, is reviewed and its implementation is described. A detailed
analysis of sources of error and estimates of uncertainty are presented. Use of the
transfer standard for measuring an arbitrary optical modulation depth is described
along with some design considerations to achieve the lowest possible transfer
uncertainty. A modification of the calibration service that allows calibration of
photoreceivers that do not provide access to the bias current is also described.
This modification, offered as a Special Test, allows the absolute responsivity of the
photoreceiver to be measured, but with degraded uncertainty due to repeatability
of the optical insertion loss of the fiber connectors.

Key words: calibration; frequency response; modulation depth; optical receiver;
photodiode; reference receiver; transfer standard

1. Introduction

Increased commercial availability of optoelectronic devices and test equipment requires the
availability of accurate and inexpensive optoelectronic frequency response calibrations that are
traceable to national standards. Examples of this need are the standard test receivers used for
SDH/SONET (synchronous digital hierarchy/synchronous optical network), Fibre Channel, and
Gigabit Ethernet that are specified [1] as having a fourth-order Bessel-Thompson filter response
with tolerances [2], [3] as low as +0.3 dB to +0.5 dB. Instrumentation for analog applications
such as CATV have comparable tolerances. Our customers prefer transfer standard receivers
that are calibrated with uncertainties that are at least a factor of 4 smaller. Until recently,
uncertainties this low were not possible[4], [5].


Appendix A: Use of transfer standard in a ratio system «0.6.66... eee cece ee eee eee ee 30
A.1 Application of heterodyne formalism to arbitrary modulation depth . .
A.2 Calibration transfer using ratio measurements ...........-+-4- .31
A.3 Sources of uncertainty in ratio measurement system .
Type of photoreceiver specimen
Spurious harmonics ........
Relative intensity noise .
Wavelength dependence
Reference 0.0... cece cece ener e rete enn enn ene e eee

Appendix B: Heterodyne system with unequal powers ........ 6.0... cece cece eee eee 35

Appendix C: The meaning of normalized response and 0dB ........... eee ence eee neee 36

Appendix D: Photoreceiver with no access to bias monitor ....... 0... 0c eee cece eee eee 37
D.1 Expression of absolute responsivity in terms of measured quantities .

D.2 Uncertainties of amplified receiver/power sensor combined response
Coupling ratio 2... cece ec eee ete eee e eee ennee

Receiver linearity .

Receiver stability .

Receiver noise

Appendix E. Sample calibration certificate 6.2.6.6... cece cece cece eee eee e ee eee 40

Appendix F. Shipping instructions

iv


going to the frequency measurement assembly to the power going to the specimen is controlled
by VBS3.

Effects which cause the modulation depth to vary from 100 % should be minimized. The optical
return loss of test devices should be higher than 20 dB to reduce multipath interference in the
fiber delivering light to the detector. Fiber connectors used should mate with minimal gap to
avoid wavelength dependence in the insertion loss. Since the power from YAG3 which is
coupled into the fiber changes when it is thermally tuned, VBS2 must be used to adjust its power
before the second part of a 40 GHz scan.

4. Uncertainty in combined photodiode/power sensor normalized response

Uncertainties in the measurement of a photodiode with a current monitor and a receiver without
a current monitor are different. Uncertainties peculiar to a receiver without current monitor will
be discussed in Appendix D. Typical uncertainties for the photodiode are listed in table I. [16]
Type A uncertainties are uncertainties that can be calculated using purely statistical analysis and
include repeatability, offset correction, and reproducibility (environmental effects). Type B
uncertainties are inferred by other means. The coverage factor of 2 gives approximately 95 %
confidence that the true value of the frequency response lies within the interval [measured value
+ expanded uncertainty] if all the uncertainties obey a Gaussian distribution. We anticipate that
most customers who are interested in calibrations of this type will be mostly interested in
uncertainties that might change the shape of the frequency response and are not as concerned
with the absolute response. The type B uncertainties that are important for this type of transfer
standard are quantities which might vary with frequency or which might change during the
measurement. Range-scaling uncertainties in the meter are included in the uncertainty budget
since the range setting might change during the measurement. The current monitor is also
included because its offset may drift. Uncertainties in the 50 MHz calibration standard in the
power meter are not usually included, although they are outlined below. A standard that can not
be connected to the 50 MHz reference calibrator introduces an arbitrary shift (or scale factor in
linear units) that can change between measurements, and which must be corrected. Optical
connector repeatability is not an issue in the normalized response measurement since the
response is normalized to the de photocurrent, which is proportional to the power actually hitting
the detector. We assume that any insertion loss in the connectors has negligible wavelength
dependence. rf power meter range scaling and bias current monitor uncertainties are the
dominant contributions to the uncertainty budget. The total uncertainty given in table 1 is the
square root of the sum of the squared uncertainties (rss). Details of the uncertainty budget are

given below.
4.1 Type A uncertainties
Repeatability: Since the heterodyne system uses a swept measurement, different scans will not

repeat exactly the same frequencies, nor will the measured frequencies exactly coincide with the
requested frequencies. Two scans are made in both forward and reverse directions, giving a total

13


where €, is the permittivity of free space, 1) is the permeability of free space, E is the electric
field vector, E’ is its complex conjugate, and & is a unit vector in the direction of propagation.
The heterodyne beat note at frequency f is generated by mixing signals from two “single-
frequency” lasers as shown in figure 1. If the laser beams have the same polarization and the
curvature and direction of propagation of the laser beams after passing through the beamsplitter
are the same (the beams are mode-matched) the electric field incident on the detector can be
written as

E(,y,1)=(Ee'TM + Ege'@?TM)F (x,y) . Q)

Equation (2) can then be integrated over the surface of the detector eliminating the spatial
dependence in F;(x,y) to give the power incident on the detector. Let the power delivered to the
detector by the ith laser be Po; = %|Egi|’4 (€/Ho)" where A = f [|F,(x,y)"dedy integrated over
the area of the detector, and Eo, is the electric field. Then the total power incident on the
detector is

Prag) = (Po, + Po2) + 2YPoPo2 cos(2T ff) . (3)

Here we have assumed that the power from
each laser is constant and that each laser is
truly single frequency. The phase relationship
between the lasers has also been neglected.

Beamsplitter

2.1 Photodiode with access to bias monitor Eopeitor270o
The photodiode in figure 1 is connected to an

external bias network and de blocking

capacitor. A dc return path must be provided .
for the photodiode, either through a bias T or Ye
through a resister or attenuator. The +V,
photocurrent generated by the photodiode due

to the optical power incident on it is given by

i(F0) = Po, + Po) RO)
2VPoPor RUF) cos(2nft+o(f))
tae * bop 4)

+

<—_i,

where R(f) is the responsivity of the detector

(in A/W) at frequency f and (f) accounts for

phase delay in the photodiode, transmission Figure 1. Simple photodiode circuit showing
line, and connectors. For the purposes of this generation of photocurrents.


The offset uncertainty can be characterized by the standard deviation of the a, Ify,, yz, .... ¥4 are
independent Gaussian random variables, the variance of the median of y,, Y», .... ¥; is
approximately equal to [21]

Now, by expanding 7( J) into a sum, we can show that
var(Q,f) - WA) ~ "vary, (49) 26)
so an estimate of the variance of a, is given by
Sy) = one , 07)

where 6? is the variance estimate of scan j given in eq (14).

Environmental conditions: Another source of uncertainty is due to environmental conditions
sich as temperature, pressure, relative humidity, and other unknown interfering factors. A
clheck standard was constructed in an attempt to evaluate these effects and to track changes in
the? measurement system. Unfortunately, each transfer standard is affected by these parameters
di{‘Terently, and it is impossible to evaluate the long term reproduceability or stability of each
cusstomer’s transfer standard. We intend that our measurements of the check standard to be used

as a! measure of the system reproducability and that the reproducability of the transfer standard
be left to the customer.

The check standard consists of two photodiodes, each with regulated bias and bias monitor
circuits. The photodiode labeled “Lowband” has a nominal bandwidth of about 16 GHz and is
connecied to a 3 dB attenuator, a 3.5 mm to N adapter, and a commercial rf power sensor
(diode) that operates between 100 kHz and 4.2 GHz. The photodiode labeled “Highband” has a
nominal bandwidth of about 30 GHz and is connected to a 3 dB attenuator and a commercial rf
power sensor (diodc) that operates between 50 MIIz and 50 GIlz. Both photodiode assemblies
are permanently mounted in a box with a power supply and access to the bias monitor and power
sensor. Measurements were made on both bands over a year’s time. Because the photodiodes
were permanently joined with the power sensor, no connection to the 50 MHz reference source
on the power meter could be made. Hence all measurements were simply normalized to the
value at 50 MHz. The nominal response curves and deviation from the mean are shown in
figures 8 through 10.

19


NIST Measurement Services:

Calibration Service of Optoelectronic NIST.
Frequency Response at 1319 nm for pene ion
Combined Photodiode/RF Power 250-51

Sensor Transfer Standards

Paul D. Hale and C. M. Wang

U.S. Department of Commerce
Technology Administration
National Institute of Standards and Technology


of the data acquisition equipment. At present, the highest resolution achievable in swept
operation is about 300 kHz. Finer resolution (< 100 Hz) is attained using a phase-locked loop
(not shown in figure 1) at frequencies between 300 kHz and 1 GHz. The lasers are intensity
stabilized so that nearly equal power from each laser is delivered to the photodiode as measured
by the bias current monitor. The combined laser beams pass through a polarizing isolator so that
the signal from each laser is in the same polarization state when it reaches the photodiode
ensuring nearly 100 % modulation depth. The total optical power incident on the photodiode is

Pratt) = (Po, + Pop) + 2fPo;Po7 cos(2nft) , (i)
and the photocurrent generated is given by
iG = Po, + PopRO) + 2fPoPopR(Neos2nft) , @

where Po, and Po, are the optical powers delivered to the detector from the lasers and R(/) is the
responsivity of the detector (in A/W) at frequency f. The first term on the right side is the dc
photocurrent, which flows through the bias supply, and the second term is the rf photocurrent
which flows through the rf load through a high-pass filter. The mean-squared photocurrent
generated by the photodiode is

< i, z= Por + Po R70) + 2Po,Po Rf) (3)

where the first term on the right side is a de term and the second is an ac term; hence

25 _ 7 22 72
Sr BSi > + <iy>. (4)

These terms are proportional to the electrical power generated by the photodiode. If Po, is nearly
equal to P,, then 2(Po,Po2) is, to first order, equal to 0.5(Po,+Po,)’. The normalized frequency
response 9t( 7°), which is defined as R*( ')/R?(0), can then be found by taking the ratio of the rf
electrical power P,, to half the de electrical power delivered to a load R,,

Py _ _ <P,
<ig>R, — 0.5<ig.>R,
___ APosPo RAR, 6
0.5(Po, + Po:)?R2O)R,
~RY
RQ)

P,,is a function of frequency. It includes corrections for sensor calibration factor and electrical

Page: Page x ofy
Calibration No.: XXXXX
Date of Report: month xx, 199x 42


2
sensorl > (8)

1
C= sll - Tal,

where k is the sensor calibration factor and I’, and T,,,,.., are complex reflection coefficients.
However, C does not need to be known and the power meter reading does not need to be

corrected with a frequency dependent calibration factor. The form of C is stated here only for
completeness.

The photodiode, attenuator or bias T, and rf power sensor can be left free to be disconnected at
the plane of the power sensor connector, or they can be permanently joined. Each of these
methods has potential trade-offs. If the power sensor is free to be disconnected, the internal gain
of the power meter can be scaled according to the 50 MHz reference source on the power meter.
This may be an advantage if the transfer standard will be used to measure modulation depth (see
Appendix A). However this introduces uncertainty duc to the disconnect/reconnect procedure
and can be operator dependent. This uncertainty is a function of frequency.

If the power sensor is kept attached to the photodiode, the internal gain cannot be scaled to the
50 MHz reference source, and long-term drifts in the gain can lead to offsets (on a logarithmic
scale) in the response. These offsets can be assumed to be independent of frequency since the
measurement is made over a short time relative to the drift. Then the offsets can be corrected
using a least-median deviation, as described in Chapter 4. This type of transfer standard
calibration would be preferred for measurements that are more concerned with the frequency
response at one frequency relative to another frequency than with the “absolute” normalized
frequency response. For example, this type of transfer standard could not be used to measure the
actual fractional modulation depth of a source, only changes in the modulation depth with
frequency (see Appendix A). The choice between these methods is left to the customer.

3. Nd:YAG heterodyne measurement system
3.1 Basic setup and swept operation

The Nd:YAG heterodyne system uses two commercially available single-mode monolithic-ring
Nd:YAG lasers operating at 1.319 jim. The system of lasers, mirrors, attenuators, acousto-optic
modulator (AOM), and beamsplitters is shown in figure 2. The laser YAG3 is a new high-power
model that replaced the laser previously called YAG1. The beam from YAG2 travels through the
AOM and is combined with the beam from YAG3 in beamsplitter BS1. The combined beams
then go through polarizing isolators. These reduce the effects of optical feedback on the lasers
and ensure that the polarization of each laser is the same before entering standard single-mode
fiber through variable focus collimators. The collimators have return loss greater than 30 dB to
reduce multiple path interference in the fibers. The AOM uses a traveling acoustic wave to
diffract a small fraction of the beam from YAG2. This beam is Doppler-shifted down in
frequency by 70 MHz and is combined with a small portion of the beam from YAG3 in


range of frequencies. This practice assumes that both systems impart negligible error at that
frequency and can be misleading.

Another method of comparison uses the absolute response. This method suffers from connector
insertion loss reproducibility and optical power uncertainty. The absolute rf responsivity is
calculated from the normalized frequency response by multiplying by the square of the de
responsivity, which is measured separately. Because most fast commercial photodetector
packages are pigtailed and connectorized, the uncertainty of the absolute responsivity includes
the uncertainty of the fiber connector insertion loss. Variations in fiber connector insertion loss
may be high and can contribute to significant uncertainties in the absolute responsivity [10], [11].
A correction must be made for these variations to attain the desired uncertainty. This problem
will be discussed further in Appendix D and Chapter 4. High speed detectors that are thin may
also have significant wavelength dependence of the absolute responsivity due to interference in
the photodiode.

2.2 Combined photodiode/rf power sensor transfer standard

Measurement of a photodiode’s unknown frequency response using a photodiode (transfer
standard) calibrated using eq (6) includes calibration uncertainty of both the power sensors used
to measure P ,, from the photodiode transfer standard at NIST and at the customer’s laboratory,
and calibration uncertainty of the sensor used to measure the photodiode, giving a total expanded
uncertainty of 0.2 dB or more for the modulation transfer function. Combined with other factory
uncertainties, this may give an unacceptable uncertainty for the intended test system.

The transfer uncertainty can be reduced by calibrating the frequency response of the photodiode
combined with the rf power sensor and bias T or attenuator used for de return. This method
totally eliminates uncertainties due to power sensor calibration and impedance mismatch. The
combined frequency response R*(f) measured on the NIST heterodyne measurement system
includes the power sensor calibration factor and impedance mismatch, and is given by

ap . 2)
RY) = =P
P 0)

m

05<i2>R, |

In eq (7), P,, is the indication of the power meter after zeroing and calibration against the 50
MHz reference signal (from the power meter) using a calibration factor of 100 %. C is given by


noise. Offset correction for the fiber connector insertion loss must be included to reduce the

relative uncertainty to an acceptable level. The uncertainty in the absolute level still remains and
can not be characterized within the tolerances that are typically required.

Coupling ratio: The coupling ratio is measured at the beginning of a measurement and then the
10 % port is monitored during the scan to infer the power reaching the receiver. The fiber-to-air
launch from the coupler monitor port into the power meter is terminated with a connector angled
at 8° to minimize coherent multiple path effects. Coherent effects due to nonzero return loss
(typically 30 dB) give repeatable systematic uncertainties of about 0.35 % (10). Coupling ratio
drift during the scan is random and is included in the repeatability described above. An additonal
error in monitoring the optical power is sometimes observed if there are etalon effects in the thin
photodiode or between the fiber and detector. This causes the optical power measured by the
monitor to be different from the actual power which is coupled into the photodiode and can be a
significant error over a large bandwidth.

Receiver linearity: Since the power detection is not frequency selective, harmonics of the
modulated signal due to nonlinearity give an error in the rf power measurement. To characterize
the receiver nonlinearity the optical power can be varied and harmonics measured on an electrical
spectrum analyzer. An optimum average optical power input is a compromise between receiver
nonlinearity and power sensor noise.

Receiver stability: Measurements at frequencies well above the amplified receiver’s cut off can
show additional instability. This may be related to the low open loop gain of the receiver
amplifier at these frequencies (see repeatability at 1500 MHz in table D1).

Receiver noise: Some broadband receivers generate noise power significantly higher than the
power sensor noise floor, giving poor dynamic range in the heterodyne measurements. Often the
noise power is stable and can be subtracted from the measured power in the heterodyne system,
giving significant improvements in the measurement dynamic range.

38


5. Quality Control

5.1 Calibration notebook

A notebook which describes the measurement setup for all calibrations, voltage range range used
for each scan and corresponding frequency range, biasing conditions, adapters, and any other
pertinent information will be kept.

5.2 Checks on each calibration

A system failure which would possibly give erroneous results occurs when the lasers are not truly
operating in a single mode. This is the usual problem in laser temperature regions where the
laser mode is unstable and near a mode hop. A spurious mode has also been observed in YAG3
for certain tuning conditions. Precautions which will be taken to ensure rejection of invalid data
due to spurious modes include checking the optical spectrum analyzer at the beginning and
occasionally during a scan.

Frequency scans over adjacent bands should overlap both in frequency and in magnitude.
Typical offset between scans is less than 0.02 dB. If the bands do not overlap, and the power
meter scale factor was not set with a different power sensor, then the operator should search for
the cause of the problem.

The bias current for each scan will be checked and should change by no more than 5.6 %.

5.3 Periodic checks

Power stability: When the data for a scan are being acquired, the total photocurrent is
monitored and during the analysis of the data it is checked to make sure it did not vary out of the
specified 5.6 % (16) total allowed deviation. However, periodically, the photocurrent of the
each laser will be monitored during a frequency scan to check for problems.

Gunn oscillator frequency: The frequency of the Gunn oscillator used for downconverting
frequencies in the 40 to 60 GHz band is subject to change with temperature and external stresses,
such as from mounting clamps. The frequency and temperature dependence of the Gunn
oscillator will be checked periodically or after major changes to its mount. This is accomplished
by mixing the oscillator’s signal with a source of known frequency near 50 GHz and measuring
the difference frequency.

Check standards: A check standard is used to verify the operation of the heterodyne system. A
fixed reference standard has been implemented (designated NIST ET) and is described in the
section on environment sources of uncertainty above. Periodic measurements on this standard
will be performed to verify the system integrity and to obtain better information on the check

26


mismatch, and is the power that would be delivered to an ideal load R,. Measurements are
typically made with transmission lines and loads with characteristic impedance of 50 Q; however
these equations also apply to measurements with 75 Q systems.

Calculation of photoreceiver’s frequency response in a ratio measurement system using the
normalized response, #7( f) would include calibration uncertainty of both the power sensors at
NIST and the customers laboratory, giving a total 20 uncertainty of about +0.2 dB. Combined
with other uncertainties, this may give an unacceptable uncertainty for the intended test system.

Instead, this calibration measures the response of the photodiode combined with the rf power
sensor eliminating uncertainties due to power sensor calibration and impedance mismatch
correction. The combined normalized frequency response R?(/) measured on the NIST
heterodyne measurement system and reported in this calibration includes the power sensor
calibration factor and impedance mismatch, and is given by

Bip = ED
Cc
2P G)

<ioR,

In the above expression P,, is the indication of the power meter after zeroing and calibration
against the 50 MHz reference signal using a calibration factor of 100%. C is a function of the
electrical vector reflection coefficients of the power sensor and the photodiode but does not need
to be known. The normalized combined frequency response may be quoted in decibels as
20log[R(f)]. All NIST calibrations report the normalized response in 20log[R(f)] format. The
electrical bandwidth of the Reference Receiver is where 20log[R(f)] falls by 3 dB from the
low frequency level.

If the power sensor and photodetector are permanently attached, the combined normalized
frequency response is further normalized to give 0 dB at 50 MHz. For more information on how
to apply this calibration in a ratio measurement system to sources with arbitrary modulation depth
consult P. D. Hale,C. M. Wang, R. Park, and W. Y. Lau, “A transfer standard for measuring
photoreceiver frequency response,” J. Lightwave Technol. 14, 2457 (1996) and NIST SP 250-

XXNX.
Procedure

The power sensor was zeroed with a Model XXXX power meter. The power from each laser to
the photodiode was adjusted to give 50 mV on the bias monitor, which was assumed to
correspond to 50 pA. Swept scans were made with data points spaced by about one tenth to one

Page: Page x of y
Calibration No.: XXXXX_
Date of Report: month xx, 199x 43


bias current and a 3 dB pad gives an error of 0.013 % at low frequencies. The background noise
is about - 40 dB (re 1 mW) for thermal power sensors.

Reference power uncertainty: If the transfer standard is of the type where the power sensor is to
be disconnected to scale the power meter gain, an uncertainty from the 50 MHz reference source
needs to be included, since it assumed that the intent of the sensor is to calculate absolute
modulation depth. The power reference accuracy is specified by the manufacturer as +0.9 %
RSS for one year and is assumed to be 10. Mismatch between the power sensor and the
reference gives an additional error. The reference is specified as having a maximum VSWR of
1.05, giving p < 0.024. The reflection coefficient of the power sensor at 50 MHz typically varies
between 0.015 and 0.03. An upper bounds for the mismatch error is |1 + (0.024)(0.03)? - 1 =
+0.0014, or £0.14 %. Modeling the distribution as uniform, gives a standard deviation of 0.08
%.

Gunn oscillator frequency drift: Uncertainty in the normalized response due to frequency drift
is given to first order by

S(10log[R2(f)}) = Sfslope. (30)

A maximum slope is about 3 dB/GHz, the drift of the oscillator is about 9 MHz/°C and the
laboratory temperature drift is about +0.28 °C worst-case. This gives an uncertainty in the
normalized response of about 0.008 dB or 0.17 %.

Hysteresis: Averaging internal to the power meter can cause the meter response to effectively
shift and smooth sharp features in the frequency response. This is avoided by using 0.01 dB
resolution, with the default averaging factor instead of 0.001 dB resolution and making two
scans in both forward and reverse directions. The result of scanning in opposite directions is to
(a) average errors and (b) flag regions where there are problems by showing large interscan
uncertainty.

Relative intensity noise: Laser relative intensity noise (RIN) could degrade the accuracy of the
heterodyne measurement system by adding a small amount of power to the measurement from
both the spontaneous-spontaneous beat note and the signal-spontaneous beat note. In the
Nd:YAG system, the signal-spontaneous beat noise causes side lobes are >30dB (re: carrier)
below the carrier at about 100 kHz offset. This places a small error on the resolution of the
system, but this error is insignificant for most real detectors. The spontaneous-spontaneous beat
noise is many orders of magnitude lower and is an insignificant source of error.

25


In the past, photoreceiver frequency response measurements have had high uncertainties for two
reasons: inaccurate knowledge of the optical stimulus and large uncertainties in the microwave
power measurement. With careful attention to system performance, uncertainties around 0.12
dB to 0.45 dB can be achieved [5]. This accuracy is not adequate to support the +0.3 dB
SDH/SONET tolerance specifications with adequate confidence.

In a well designed heterodyne measurement system, the variation in optical stimulus can be
reduced to +0.0023 dB (coverage factor k= 1). Typical rf power sensor calibration uncertainties
are about a factor of 15 or 20 higher (for k= 1). Uncertainties due to mismatch can be 0.1 dB or
higher. Mismatch errors can be corrected, but it is unclear whether the uncertainty in the
corrections is low enough to give adequately improved uncertainty. If the uncertainty due to rf
calibration and impedance mismatch could be eliminated, the overall optoelectronic response
uncertainty could be significantly reduced.

In this work, we describe a method for calibrating a photoreceiver frequency response transfer
standard with the low inherent uncertainty of a Nd:YAG heterodyne system. This is achieved by
combining a photoreceiver with a microwave power sensor and calibrating the response of the
combined unit, eliminating rf sensor calibration and mismatch uncertainties. The measured
response is normalized to the dc electrical power generated in the photodiode to give the lowest
possible uncertainty. The Nd:YAG heterodyne measurement system is also described along
with a detailed uncertainty analysis for calibration of a combined photoreceiver/power sensor
transfer standard. The theory for measuring an unknown device against the transfer standard
and measurement of modulation depth is also derived.

Calibration of frequency response normalized to the optical power is also described. This type of
normalization gives absolute responsivity, but with a degraded uncertainty, and is especially
suited to calibrations of amplified photoreceivers. It is offered as a Special Test because the
uncertainties due to fiber connector insertion loss can not be fully evaluated.

2. Principle of heterodyne frequency response measurements

The advantages and disadvantages of various methods for characterizing photoreceivers have
been discussed by several authors [4], [6], [7]. The main advantages of the heterodyne method
are that the optical modulation is completely calculable from fundamental principles, it gives
results directly in the frequency domain where many industrial specifications are written, and
tuning ranges are available over 65 GHz or more. The heterodyne principle is based on a
property of all optical quantum detectors: the current generated by the detector is proportional to
the time-averaged energy flow (S) integrated over the surface of the detector. Here S is the
Poynting vector and its time average (assuming a monochromatic plane wave) is [8]

(S) = i]s (BE Yk @)
2\) Ho


0.162 42.0%

MSE(x) = 0.004 685b4c? + ;
ni

(12)

where ¢, is the second derivative of R?(y) evaluated at y = x using a spline method and 0” is the
variance of the response of a given scan. This variance, however, is unknown and needs to be
estimated. A technique [20] that works well and can be used to obtain an estimate of 0” is to

“detrend” the data locally and use the sample variance of the detrended data. The detrended
residual value at f; is defined as

RG) + PG)

= Ry -
= BY) 3

(13)

and the variance estimator is found by

al
2

Si
7. 2) im

(14)

Let R (x) and MSE,(x) be the estimated response and the mean-squared error at frequency x of
the ith scan. The estimated mean response based on m scans is

Zo >) R; @) as)
m

and its standard error is
s(x) = six) + s(x) ; (16)
m
where
(RB; x) - RG)? (17)
ns

16


2R,P pur

2 p2 .
Mo Pivg:put

Ghul) = (A13)

A.3 Sources of uncertainty in ratio measurement system

The following is a brief list of error sources that must be considered when designing a ratio test
system.

Type of photoreceiver specimen: Equations (A9), (A10), and (A13) include the rf power
measured from the DUT. If the DUT is a photoreceiver, the power must be measured with some
kind of electrical transducer that will indicate how much electrical power is being generated. The
calibration factor and impedance mismatch of this transducer must also be included in the
customer’s error budget. However, if the DUT is a device such as a lightwave communications
analyzer or lightwave spectrum analyzer, which includes the transducer, the frequency response of
the device as a whole is measured, eliminating calibration factor and mismatch uncertainties.

Spurious harmonics: Nonlinearities in directly modulated lasers, over driving, or inaccurate bias
of external modulators can cause some harmonic content [A1]. The rf signal generator can also
be a source of spurious harmonic and nonharmonic signals. Since the rf power sensor is not
frequency selective, energy at spurious frequencies gives a systematic error. Assuming that the
power sensor acts as a true rms detector, the powers add arithmetically. To keep the increase in
uncertainty below 10 %, the total harmonic power must be more than 22 dB lower than the
fundamental.

Relative intensity noise: Again, energy at frequencies other than the modulation frequency can
give systematic errors.

Wavelength dependence: Wavelength dependence of a photodiode is a complicated function of
the depletion region thickness, intrinsic layer thickness, bias voltage, and other parameters. The
variation in response due to wavelength can be as much as several tenths of a decibel [A1]. Etalon
effects inside the detector can cause relatively large changes in the dc responsivity in a way which
is not directly measured if the bias current is not monitored. This effect can be minimized by
operating the ratio test system at the same wavelength as the original calibration or corrections
can be performed if the transfer standard can be accurately modeled.

Reference
Al. Hale, P. D.; Humphreys, D. A.; Gifford, A. D. Photodetector frequency response

measurements at NIST, US, and NPL, UK: preliminary results of a standards laboratory
comparison. Proc. SPIE, vol. 2149, pp. 345-355; 1994.

33


CS)

Modulated
source

rf signal
generator

Fiber |
coupler

| Transfer rf power
(— standard meter
co
Computer

Figure A1. Ratio measurement system.

|

|

4 DUT

Power

transducer

7

34


0.04

Deviation from mean, dB

-0.04 1 T 1

Frequency, GHz
KH August 4, 1997

0.01

March 3, 1998

January 42, 1998
= October 27, 1998

December 2, 1997

-0.002 —

ApritJune, 1994

Average deviation from mean, dB
°
[=]
i=]
nN
|

-0.006 1 1 1

18 24

Témperature, deg” =

Figure 10. Top graph shows the deviation from mean of measurements on the check standard
lowband. Influence of measurements made 8/4/97, 4-6/98, and 11/10/98 is clearly
seen. When these data sets are dropped, 20 is about 0.05 dB. Bottom graph shows
correlation between temperature and average offset from mean of data sets. Error
bars are one standard deviation of the data and do not include inaccuracy of the
thermometer.

22


National Institute of Standards and Technology Special Publication 250-51
Natl. Inst. Stand. Technol. Spec. Publ. 250-51, 51 pages (Dec. 1999)
CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 1999

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325


Temperature contro! computer Data acquisition
Fast | RF
aA ( F photodiode counter
iy D =.
Intensi
control loop A I
i roL Bias supply with
YAG#1 L = 7 TA monitor
BS '
50/50 F
BS
A
‘ I ;
‘ast RF
, D photodiode |—] Power |——'
Intensit ! DUT sensor
control loop
YAG #2 ~~
Ass ae

Figure 1. Simplified schematic of the NIST Nd:YAG heterodyne system. Labeled components
are beamsplitter (BS), mirror (M), isolator (1), lens (L), fiber (F), large area detector (D), and
integrating amplifier (A).

Above 40 GHz the noise of the power sensor becomes the dominant uncertainty.

Results for this Calibration are reported in a graph on page 8 of this report and on a 3.5 inch DOS
compatible disk in ASCII format.

NIST Nd:YAG heterodyne measurement at 1.319 pm

NIST uses a Nd:YAG heterodyne system for measuring scalar frequency response because the
excitation of the detector can be calculated from first principles. A schematic of the heterodyne
system is shown in Figure 1. The system uses two single-mode monolithic-ring Nd:YAG lasers
operating at 1.319 ym. The frequency of cach laser can be tuned thermally to give beat
frequencies between dc and 65 GHz; the beats have a bandwidth of the order of 10 kHz. The
beat frequencies below 40 GHz are measured with an rf counter. Frequencies above 40 GHz are
down converted to a frequency that the counter can measure by mixing with a Gunn oscillator
operating at 62.14 + 0.015 GHz. As the frequency is scanned, data are acquired automatically.
The resolution of the system is limited by the scan rate, the frequency jitter, and the time constants

Page: Page x ofy
Calibration No.: XXXXK
Date of Report: month xx, 199x 41


Table D1. Summary of typical frequency response measurement uncertainties for the amplified
photoreceiver (nominal bandwidth of 0.8 GHz) with thermal rf power sensor.

Source of uncertainty Uncertainty,
k=1,%
Type A
Measurement repeatability @ 0.010 GHz 0.05
@1.5 GHz 11
Offset correction s, 0.007
Environmental effects s, (fin GHz) 0.106 + 0.00064 f+
0.00024 f?
Type B
Meter scaling 0.5
Meter offset 0.023
Coupling ratio 0.35
Optical power drift (power matching) 0.06
Receiver linearity, estimated from proto 900 0.1
Power sensor noise, @ 0.01 GHz 0.2
@1.5 GHz 3.8
Total uncertainty, @ 0.01 GHz 0.66
@ 1.5 GHz 4.0
Expanded uncertainty (coverage factor k= 2), @ 0.01 GHz 1.3 (0.06 dB)
@1.5 GHz 8.0 (0.34 dB)

39


50 GHz R520), ~ 2.4(m)
it ter

Amplifier lapter 40 GHz

Detector

mS K—< Ld _ ~~~ Qptical input
1.85(m) to WR-19 Adapter S \ from Lasers

40-60 GHz Mixer

62.15 GHz

Gunn Oscillator

40 GHz RF Counter

26 GHz
Amplifier

q Input 4
33 GHz Bandwidth

Coaxial Cable

Figure 4. Subassembly for measuring frequency between 40 GHz and 58 GHz. System actually
operates down to about 36 GHz.

Three generic types of open loop sweeps can be performed. The first is a scan of up to 40 GHz
in 2 parts through a mode-hop. The temperature of both lasers is initially set so that the
difference frequency is about 40 GHz. This positions each laser at the extreme end of the
temperature range where single-mode operation is possible. YAG2 is then scanned toward the
opposite end of its stable region ending with a difference frequency around 18 GHz. YAG3 is
then shifted by about 20 GHz, and YAG2 is tuned back to where it started. At this point VBS2
must be manually adjusted to compensate for the changed power from YAG3 that is coupled into
the fiber going to the photodiode specimen. We believe that the direction of the beam from
YAG3 changes slightly when the laser’s temperature changes, causing the power that is coupled
into the fiber to change. If YAG2 is ever replaced with a similar new laser, this problem must be
corrected. YAG2 is then scanned as before with a starting frequency near 20 GHz and sweeping
through dc. When diode power sensors are used, the sweep is usually done too quickly to
reliably change input ranges on the counter to measure frequencies below 500 MHz, causing
some drop-outs in that region. The finest sample spacing achievable without using an external


These scan options are accessible through a user interface program called HETSETUP.BAS.
This interface program is designed to be run as an executable which calls other programs, also in
compiled executable form, which run the different scan options listed above. The measurement
number is recorded in a master file and is incremented with each scan, so that subsequent
measurements use a unique file number. A setup file for each calibration records the file numbers
that were used for that calibration along with the detector name and type and customer name.
Data files generated by the programs described above contain the corresponding setup file name,
data file name, temperature, and relative humidity for the scan. The files then split into four
columns that contain frequency (in gigahertz), rf power (in decibels with respect to 1 mW),
current (in amperes), and normalized response (in decibels).

3.2 Phase-locked operation

Measurements with resolution of about 100 kHz are desired at low frequencies but the minimum
practical resolution for swept measurements is greater than 30 kHz, giving the final data spacing
of about 300 kHz. A method that gives very fine resolution and solves problems related to
scanning the beat frequency through de is to synthesize the beat frequency between the two
lasers using a phase-locked loop. Early work demonstrating phase-locked operation of two
nonplanar Nd:YAG lasers operated at low frequencies and displayed small capture ranges. Later
work by several authors [12], [13] showed broadband operation above 10 MHz. However, most
high bandwidth phase-locking circuits have minimum operating frequencies of a few tens of
megahertz and are not suitable at the relatively low frequencies required for some applications.
We have solved this problem by generating a secondary optical signal whose frequency is offset
from the main signal by 70 MHz (see figure 2). The phase locking electronics then see a signal
near 70 MHz when the offset frequency of the main signal is very low.

The electronics for the phase-locked loop (PLL), shown in figure 6, were developed by the Time
and Frequency Division at NIST [14], [15]. The local oscillator (LO) is offset from the rf
frequency by 15 MHz (see figure 5). The difference frequency between the LO and rf signals is
sent to a phase comparator to compare with an inexpensive TTL oscillator operating at 55 MHz,
and generates an error signal that is filtered and fed back to the laser frequency control. For the
sign of the error signals used the beat frequency f2 at BS2 is offset from 1 ( at BS1) by 70 MHz
and is offset from the LO by 15 MHz. For the main signal at BS1 to have a frequency of 1 MHz,
the beat frequency at BS2 is 71 MHz and the LO is set at 16 MHz. The frequency stability is
limited by the relative stability of the 55 MHz TTL oscillator, 70 MHz crystal oscillator, and
synthesized LO. We have not attempted to stabilize these oscillators relative to each other.

Phase-locked frequency control in our heterodyne system works well between about 300 kHz

and 1 GHz. Unfortunately, phase-locked operation below 100 kHz is unstable, probably due to
coupling between the laser relaxation oscillations and the phase detection circuit.

11


NIST Special Publication 250-51

NIST MEASUREMENT SERVICES:

Calibration Service of Optoelectronic
Frequency Response at 1319 nm for
Combined Photodiode/RF Power
Sensor Transfer Standards

Paul D. Hale and C. M. Wang

Optoelectronics Division

Electronics and Electrical Engineering Laboratory
National Institute of Standards and Technology
325 Broadway

Boulder, CO 80303-3328

December 1999

ONT OF C,

RS yw

o

"Me
%,
Mica 4

*
nF Gp,
* “t,

.
STaTes oF

U.S. Department of Commerce
William M. Daley, Secretary

Technology Administration
Dr. Cheryl L. Shavers, Under Secretary of Commerce for Technology

National Institute of Standards and Technology
Raymond G. Kammer, Director


P

mref

1

RD] 0.5 <ferej> Ry

f

Mg = (A8)

The normalized response of the DUT is then found using eq (A5), the de photocurrent, and the rf
power (including all calibration factors) from the DUT

1 Py
Rou) = || 2" —_. (A9)
Mo} 05 <iepurTM Ry

In some test applications it may be preferable to measure the DUT’s frequency response in terms
of the coupling ratio instead of the bias current or average power. This may be the case when the
DUT has poor de stability or when the frequency response will be normalized to the response at a
specific frequency (eliminating the coupling ratio). In this case eqs (A8) and (A9) can be
combined to give

P
Rou) = SO RA) Be (A10)

mref

where f is the ratio of the optical power coupled to the reference arm to the power coupled to the
test arm.

In the case of the amplified receiver described in Appendix D the combined response of the DUT
is

gy - FO

2R,P, (All)

and can be used to find the modulation depth of the source from the equation

2R, P.
2 mre}
Mg = > a (A12)
& A Pogref

The DUT’s response is then

32


Mean normalized response, dB
&
|

-20 qT | ' 1 q

Oo

20 40
Frequency, GHz

60

Mean normalized response, dB
1

1.6 T T T T T T T T T
1 4

oO

2 3
Frequency, GHz
Figure 8. Mean normalized response of the check standard shifted to give 0 dB at 0.05 GHz.

Upper graph is highband, and lower graph is lowband.

20



| he National Institute of Standards and Technology was established in 1988 by Congress to ‘‘assist industry in
the development of technology . . . needed to improve product quality, to modernize manufacturing processes,
to ensure product reliability . . . and to facilitate rapid commercialization . . . of products based on new scientific

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of the agency’s basic functions is to develop, maintain, and retain custody of the national standards of
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manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal

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As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and
applied research in the physical sciences and engineering, and develops measurement techniques, test
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‘At Boulder, CO 80303,
Some elements at Boulder, CO.


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5. Gifford, A. D.; Humphreys, D. A.; Hale, P. D. Comparison of photodiode frequency
response measurements to 40 GHz between NPL and NIST. Electron. Lett., vol. 31, pp.
397-398; 1995.

6. Hale, P. D.; Franzen, D. L. Accurate characterization of high speed photodetectors. Proc.
SPIE, vol. 2022, pp. 218-227; 1993.

7. Bowers, J. E.; Burrus, C. A. Ultrawide-band long-wavelength p-i-n photodetectors. J.
Lightwave Technol., vol. 5, pp. 1339-1350; 1987.

8. Wangsness, R. K. Electromagnetic Fields. New York: John Wiley & Sons; pp. 440-443;
1979.

9, Fundamentals of rf and microwave power measurements, Hewlett-Packard Application Note
64-1A; 1997.

10. Wong, B.; Kosiorska, H. Factory measurement solutions to predictable field performance
of single mode fiber optic connectors. Day, G. W.; Franzen, D. L eds. Technical digest-
Symposium on optical fiber measurements; 1992. Natl. Inst. Stand. (U. S.) Technol. Spec.
Publ. 839; pp. 23-28; 1992.

11. Gallawa, R. L.; Li, X. Calibration of optical fiber power meters: the effect of
connectors. Appl. Opt., vol. 26, pp. 1170-1174; 1987.

12. Kazovsky, L. G.; Atlas, D. A. A 1320-nm experimental optical phase-locked loop:
performance investigation and PSK homodyne experiments at 140 Mb/s and 2 Gb/s. J.
Lightwave Technol. vol. 8, pp. 1414-1425; 1990.

13. Williams, K. J.; Goldberg, L.; Esman, R. D.; Daagenais, M.; Weller, J. F. 6-34 GHz offset
phase-locking of Nd:YAG 1319 nonplanar ring lasers. Electron. Lett. vol. 25, pp. 1242-
1243; 1989.

14. D’Evelyn, L.; Hollberg, L.; PoPovic, Z. B. A CPW phase-locked loop for diode-laser
stabilization. IEEE MTT-S Int. Symposium Digest, San Diego, pp. 65-68; May 1994.

15. D’Evelyn, L. Noise characterization of extended-cavity diode lasers using a new phase-
locked loop for diode laser stabilization. M.S. Dissertation, University of Colorado,
Electrical and Computer Engineering Dept.; 1994.

16. Guide to the expression of uncertainty in measurement. ISO, Geneva; 1993.

17. Silverman, B. W. Density estimation for statistics and data analysis. London: Chapman and
Hall, pp. 34-72; 1986.

28


Appendix D: Photoreceiver with no access to bias monitor
D.1 Expression of absolute responsivity in terms of measured quantities

Some optical receivers will not allow access to the de photocurrent or bias current. In this case it
is neccessary to measure the rf power generated relative to the optical power incident on the
receiver. Since most high speed receivers are fiber-pigtailed and connectorized, it is difficult to
measure the exact optical power that is incident on the receiver because of poor connector
repeatability. This Appendix considers this situation. At this time, measurement of a receiver that
does not have access to the bias current is offered only as a Special Test. It is desirable in some
applications to know the absolute voltage response of the photoreceiver. An amplified
photoreceiver commonly requires this type of characterization. This Appendix will demonstrate
the formalism used in calculating voltage response.

For a photoreceiver without a bias current monitor, the system in figure 1 includes a 10 dB
(nominal) optical coupler that monitors the total power from the lasers during a frequency scan.
The power incident on the DUT is inferred from the coupler monitor port. The voltage that the
receiver delivers to a load R, is given by

VA t) = Por + Poz)G0) + 2yPo,Po,G(f)oos(2mft) , @1)

where G(f) is the amplified response of the detector (in V/W) at frequency f. The first term on the
right side is the average dc signal, and the second term is the rf signal. The voltage response is
found in a similar manner to eq (6) and is
2R,P,
2, - Le of
Gf) = —*, (D2)

avg

where P,,, = Po; + Po2 is the average (dc) optical power incident on the detector and P, is the
electrical power delivered to a load R, (the power sensor). This ratio is insensitive to small
changes in power from either laser because the powers from the two lasers are nearly equal. If
the voltage response is measured in dB (re 1 V/W), rf power in decibels (re: 1 mW), the average
optical power is in decibels (re: 1 mW), and R, = 50 Q, eq (6) can be written as [2]

2Wlog(G(f)) = 50 + O, - 2,4 » (D3)
where ® denotes a power measured in decibels (re: 1 mW).
D.2 Uncertainties of amplified receiver/power sensor combined response

Typical uncertainties for the receiver are listed in table D1. The dominant uncertainties are fiber
connector insertion loss, power meter scaling, coupling ratio measurement, and power sensor

37


Measurements on the highband photodiode consisted of swept scans over the following
approximate ranges: 50 MHz to 1 GHz, 500 MHz to 40 GHz, and 38 GHz to 55 GHz. Two
scans were made in both forward and reverse directions, giving a total of four scans in each
range. The room temperature and relative humidity were measured before each scan. Where
scans overlap in frequency, the lower frequency scan was always used in the final analysis. A
plot of the deviation from the mean (see figure 9) shows monotonically increasing uncertainty
with frequency with large spikes near 43 and 52 GHz where the frequency response of the
standard has notches. There is not a jump in the deviation in the region of 40 GHz, where
frequency is measured with the Gunn oscillator and mixer, showing that frequency accuracy is
not a major problem in the 40 to 55 GHz region, although this may be part of the reason for
large uncertainties at the notches at 43 and 52 GHz. The measurement performed on July 25,
1997, shows a significantly higher deviation than the other scans below 23 GHz, but then is in
the middle at higher fequencies. If this data set is neglected, the 10 deviation from the mean fits
roughly a second-order polynomial in frequency,

S(f =a +aftaf?. (28)

Measurements on the lowband photodiode consist of a swept scan over the range of a few
megahertz to 4.2 GHz and a set of data acquired using the phase-locked loop between 300 kHz
and 600 MHz. Swept measurements were made in the forward and reverse directions giving a
total of four scans and three sets of data were acquired using the phase-locked loop. A plot of
the deviation from the mean (see figure 10) shows that measurements taken on August 28, 1997,
fall above the mean and measurements in April/June 1998 fall below the mean. Both data sets
have a large ripple indicating that the ripple in the frequency response was distorted in these
measurements. In an attempt to find a correlation between room temperature and these
deviations, the average temperature was plotted against the average deviation for each data set
showing a possible trend. A final measurement taken November 10, 1998, with the room
temperature intentionally lowered appears to confirm the trend. Whether this trend is the cause
of the slightly higher value in the data below 23 GHz in the highband data is unkown.

Since the lowband data for August 28, 1997, and April/June 1998 were shown above to be
outliers, they can be discarded. Then the data from the lowband measurements and highband
measurements are consistent and the expression for the environmental random variation in eq
(28) is still valid if the laboratory temperature stays at 21.55 + 0.28 °C. It is possible that
environmental uncertainty is mostly due to environmental effects on the check standard and not
on the measurement system. However the check standard is the most stable device that we have
been able to construct, and its stability cannot be measured independently from the stability of
the measurement system. Until a better check standard is available, the reproducability of the
check standard measurements will be used as a measure of the system stability. This is a good
assumption since the contribution of s, is not really significant below about 40 GHz.

The combined type A uncertainty is then found by adding the components of uncertainty in
quadrature [14]. That is, we use

23


Intensity control

loop
an
x FC to fast detecter,
rs C couriter, and PLL
Intensity control o oH
loop T

4 AOM 1 FC

vac |--~-

S19
<j

To specimen, spectrum
anlayzer, and optional
power meter

70 MHz Osc.

Detector to PLL
(Figure 4)

Figure 2. Schematic of heterodyne measurement system. Labeled components are beamsplitter
(BS), variable beamsplitter or variable attenuator (VBS), mirror (M), acousto-optic
frequency shifter (AOM), neutral density filter (ND), half-wave plate (HWP), isolator
(D, and fiber-collimator (FC).

beamsplitter BS2. The resulting beat note, which differs in frequency vy /U MHz from the main
signal at BS1, may be used for phase locking the lasers and controlling their frequency difference
with a frequency-synthesized signal generator. This option will be discussed in section 3.2.

The frequency of each laser can be tuned thermally to give beat frequencies from nearly de to
greater than 55 GHz; the beats have a short-term bandwidth of less than 3 kHz. The beat
frequency is measured with a microwave counter (see figure 3). As the frequency is swept, data
are acquired automatically. The data spacing is usually selected to be one-tenth to one-fifth of the
customer’s requested data spacing. The frequency resolution of the system is limited by the
sweep rate, the frequency jitter, and the time constants of the data acquisition equipment. At


Appendix F. Shipping instructions

Equipment should be shipped in well-padded foam, or otherwise mechanical-shock insulated
cases, appropriase for reshipment back to > the customer. Operation instructions or instruction

The customer should
include all cables and connectors that are necessary to calibrate the equipment as specified.
Depending on the power meter model and manufacturer, it may be necessary to include the
power meter and instruction manual.

47


Synthesized signal

generator
8 dBm
Optical signal
from BS2 PLL box detailed in Figure 6
Lo on/off
. . RF Power
1 GHz receiver Bias T RF kg ___ supply
Fast Out
] ye ‘ast Out F Manual gain
adjust
Monitor
h———> YAG3 piezo input
4100kO 20 second

time constant

8.25 kQ
YAG2
5kQ / > thermal
tuning
1.87 kQ

DIA Vv

YAG3
thermal
tuning

Figure 5. Schematic of circuit for frequency control, including phase-locked operation. Power
supply for PLL box is turned off for swept (open loop) operation.

Computer

voltage divider is about 5.8 MHz using the 1.5x external amplifier, giving the finest calibration
data spacing of about 45 MHz.

The second type of scan is designed for finer resolution scans and can automatically switch
between counter inputs to select the correct operating frequency range. YAG3 is left at one
position and YAG2 is swept to achieve sample spacing as low as 30 kHz. The finest frequency
resolution attainable in an open loop or swept mode can be achieved by attenuating the input to
the external amplifiers for YAG2 using the 1.87kQ/8.25kQ divider shown in figure 5.

The third type of scan is used for the 40 to 60 GHz band and uses the external mixer with the
counter (see figure 4). The measured frequency is corrected for the Gunn oscillator frequency to
give the actual optical beat frequency. In this case YAG3 is cooled and YAG2 is swept to
achieve sample spacing of about 5 MHz.

A fourth option is a phase-locked mode which steps to specific frequencies. It can synthesize

specific frequencies between 10 Hz and 1 GHz. Phase-locked operation is described in the next
section.

10