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Pulsed Doppler Lidar Airborne

Scanner

Progress Report No. 35

January - September 1985

Prepared for

George C. Marshall Space Flight Center

NASA

Huntsville, Alabama 35812

Prepared by

C. A. L)iMarzio

D. B. McVicker

C. E. Morrow

C. C. Negus

Raytheon Company

Equipment Development Laboratories

Electro-Optics Systems Laboratory

Sudbury, Massachusetts 01776

Contract No. NAS8-33120

ER85-4352

10 October 1985

-33_)-
Raytheon

Pulsed Doppler Lidar Airborne

Scanner

Progress Report No. 35

January - September 1985

Prepared for

George Co Marshall Space Flight Center

NASA

Huntsville, Alabama 35812

Prepared by

C. A. L)i/Vtarzio

D. B. McVicker

C. E. Morrow

C. C. Negus

Raytheon Company

Equipment Deveioprnent Laboratories

Electro-Optics Systems Laboratory

5udbury, ktassachusetts 01776

Contract No. NAS8-33120

ER85-_352

10 October 1985
1. INTRODUCTION

This report covers the work accomplished during the reporting period on the

subject contract and describes plans for the next reporting period. The

objectives during the current phase of the contract are divided into four phases.

Phase 1 includes ground testing of the system and analysis of data from the 1981

Severe Storms Test Flights. Phase 2 consists of preflight preparation and

planning for the 1983 flight series. The flight test itself will be performed

during Phase 3, and Phase 4 consis.ts of post-flight analysis and operation of

the system after that flight test.

Section 2 describes the work performed during the present reporting period,

and Section 3 provides plans for the next reporting period.

2. WORK PERFORMED

2.1 DATA ANALYSIS

2.1.1 RANGE PERFORMANCE AGAINST nIFFERENT TARGETS

Figure l shows the range crofile from five samples zaken dur;ng Flight ]0,

around 1700 Z. The lowest curve is taken from data collected upwind of Mr.

Shasta at about lO,O00 feet of altitude, in a clear atmosphere, where no signals

were observed. It thus is a good representation of the noise level as a function of range. The next curve was taken downwind of the mountain, and shows

evidence of atmospheric returns. There is some question as to whether the

data are valid at all ranges, or some ranges are contaminated by the others.

The top three curves show the returns from Mt. Shasta at 8 to lO kilometers. These demonstrate several features of the time history of the pulse.

There is a "shelf" about 3 kilometers long, 9 dB below the peak of the pulse,

and ringing after the pulse with a peak about 12 dB below the level of the

pulse with a decay time of 33 microseconds and a oeriod of almost l kilometer

(6.7 microseconds) corresponding to a frequency of 150 kHz. The ringing does

not decay to zero, but is still some 5 dE above the noise at the end of 200

microseconds.

2.1.2 ANALYSIS OF PULSE SHAPE

Pet. EQuiv. Rel. Rei. Energy Total Rel.

Level Time Range Power per Gate Energy

mV usec km dB dB dB

Pulse Start 142 0 0 0

End 78 2 -0.3 - 2.6 0 0

Tail Start 78 2 -0.3 - 2.6 - 2.6

End 0 4 -0.6 -4.5

Shelf Start 0 -78 ll.7

End 14 0 0 -lO.O - g.O 3.9

Ringing Start

Half

I/e

Total*

* Average over

Peaks ÷ Nulls

6 4 -0.6 -13.7 -12.6

3 24 -3.6 -16.8 -15.6 -

2_2 33 -4.9 -18.1 -17.0

-4.0

Photographs of the pulse shape were taken by placing the Rockwell detector

in front of the telescope with an aperture of a few millimeters and connecting

the detector to an oscilloscope. The two channels of the scope were connected

together to increase the gain, so that the pulse peak and the power before and

after it were measurable. Several photos were taken with different vertical

and horizontal scales and with different delays, to provide a time history o_

the entire pulse. These are shown in Figure 2. The center photo shows the

entire time history. In this case, the pulse is barely visible in the t_ird

major box from the left. The lower two photos expand the regions before and

after the pulse, and the top photo shows the detail of the pulse itself.

The above table shows the results of analysis of the photographs of the

pulse shape. The photos are considered to be divided into four parts. The

first is the "shelf" which precedes the pulse. This occurs because the amplifiers are turned on prior to the optical pulse, in order to generate the
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5 mV/D IV

PRE-PULSE

BEHAVIOR

20Fs/O IV

5 mV/D IV

RINGING

AFTER PULSE

20/.zs/D IV

5 mV/D IV

Figure 2,

Pulse Shape Photos Taken at MSFC in January !985

EO-2Oql
required gain. Unfortunately, this gain also amplifies the leakage :nrough

the modulator. The shelf is described to a first approximation as being triangular, and the table shows the start and end of the shelf.

The second region is the pulse itself, which is again described in

trapezoidal approximation. The details of this region were taken from the

top photograph. The third region is the tail of the pulse, before the

ringing begins to be noticeable.

Finally, the ringing region is considered. This region is caused by

mechanical ringing of the modulator, and is characterized by sinusoida] modulation at a frequency of 150 kHz, which has a period of 6.6 microseconds, corresponding to 9go meters of range. The envelope of the ringing is described

by an exponential function, with the decay time calculated by measuring the

time required to decay to half-height. The total energy is obtained by dividing the integral of the power envelope by two to account for averaging over

many cycles.

The immediate conclusions of this analysis are that the shelf can contribute to a spurious signal at a range before a hard target if the signal from

that target is more than 9 dB above the noise. Furthermore, it will contribute

a false velocity in this region if the hard target signal is more than 9 dB

above the atmospheric signal from a range gate in the region. Finally, it

will cause a similar effect in atmospheric signals if there are about eigmt

or more range gates beyond the one being considered which have signals comparable

to the current one. The total energy of 3.9 dB above the energy in the signal

pulse means that in many cases, the signal will be corrupted by energy from

this region.

These conditions also hold for the ringing, except that the signals will

be corrupted at ranges beyond the source of the signal rather than before it,

and the magnitude of the effect will be smaller because of the lower powers

and energies in this region.

Application of these results to specific atmospheric measurements will be

the subject of later work.
Figure3 showstheamplitudeasa functionof locationfor twoforward

andtwoaft scans.Theflight pathwasfromleft to right, acrossthebottom

of theplot. Theambientwindwasfromright to left at about220degrees

relativeto truenorth. It is evidenthat theatmospherewascleanandtna:

nosignalsweredetectedupwindof themountain.Thestrongmountainreturns

arevisible abouta quarterof thewayfromtheright-handedgeof the

pictures. Notethat increasingdarknessindicatesincreasingamplitude.The

shelfbeforethepulseandtheringingafterwardareclearlyevident. Before

themountainsignalsareobserved,thereis anincreasein thesignalat near

ranges,apparentlydueto increasedbackscatterin theair whichhaspassed

overandaroundthemountain.It appearsthat this occursat progressively

shorterrangesastheaircraft approachedthemountain,andthat theair became

toocleanto providea signal,somewhere abreastof themountain.Theaft scans

Showa similarbehavior.In addition,severalscansarecontaminatedbystrong

groundreturnsat longranges.

Figure4 showsthecorrespondingvelocityplots. At therangeswhere

theintensitiesareenhanced, upwind(left) of themountain,therearevariations in thevelocitycomponent whichmaybeattributedto a wakecausedby

themountain.Whenthemountainis visible in thescan,thevelocityof the

mountainis normallyobtainedat all ranges.Thisvelocityhasbeenexamined

in printoutsof thedata,andfoundto bewithinhalf a meterpersecondof

zero. Lightercolorsrepresentapproaching(positive)velocitiesanddarker

onesrepresentrecedingvelocities. Thevelocitieswereobtainedfromthe

VELOCITY databychangingthesignontheforwardscansonly,andaddingthe

valueof OFFSET.

2.1.3 DECONVOLUTION OFRANGEDATA

O_e_ themajordeficienciesof datacollecteddu:',n_t_e19B4

flignt _:_z&;_ theexistenceof spuriousdatadueto thefailure of the

electro-opticmodulator.It is believedthat a largenumber of themeasured

velocitiesarestill valid, andthat deconvolutiontechniquesmaybeusedto

determinethedatavalidity, therebymakingmostof this datausablefor

meteorological studies.
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1
The problem may be summarized as follows: in normal operation, the lidar is

a pulsed Doppler lidar, and returns processed in a particular range gate (a given

time interval after the transmitter pulse) may be unambiguously associated with

a range from the sensor determined by the given round-trip transit time. After

the failure of the electro-optic modulator, a substantial amount of energy was

transmitted both before and after the main pulse. Thus, in any range gate, the

return signal is a sum of contributions from different ranges along the line

of sight. In particular, at longer ranges where it is anticipated that there is

no useful signal, contributions from the closer ranges, resulting from energy

transmitted after the pulse, will often produce an apparent signal. The problem

then is to determine how far out in range this signal is to be believed.

The deconvolution techniques to be described below offer hope for resolving

some of these questions. If full spectral data were available, it would be

possible to perform a complete deconvolution and recover almost all of the lost

information. However, in the system as it was used in 1984, only spectral

parameters are available. Nevertheless, it is still possible to recover a

considerable amount of useful information from careful evaluation of these parameters as functinns of range. The approach involves making assumption about the

missing spectral information on the basis of available parameters. In this way,

it is possible to establish varying degrees of confidence in the deconvolved data

at different ranges.

2.1.4 DERIVATION OF THE CONVOLUTION EXPRESSION

The signal-to-noise ratio at any point in time after the transmitted pulse

is an integral of contributions over all ranges from 0 to infinity. The average

signal-to-noise ratio in a particular range gate is the average of the signal-tonoise ratio over that particular range gate. This can be represented-by the

following equation, as shown in Figure 5.

tg - T

SN_ m = _1 /t 2 _0 == nPC_t) hvB _dp dc d_g

(1;
Z

O

2R

tr = tr + _--

CONTRIBUTION TO

RANGE GATE AT 15kin

S (tr) = FPdF

tt, TRANSMISSION TIME

2R

P IS THE TRANSMITTER POWER AT TIME tr -

F IS THE HETERODYNE COLLECTION FACTOR

dF = X_..__b _(_.) dR I0 -2aR/10

R2+ b2

b = RAYLEIGH RANGE = 3023 METERS

a = ATTENUATION COEFFICIENT, dB/_m

_(tr) = BACKSCATTER COEFFICIENT, m-lsr -I

Figure 5. Calculating the Contribution to a Range Gate

10

EOA-4705
where T is the duration of a range gate,

is the overall system efficiency,

p(_t) is the power transmitted, which is a function of the time at which

it was transmitted,

h_ is the energy of a photon,

B is the bandwidth,

F(_) is the fraction of the transmitted power which is returned in such

a way as to mix efficiently with the local oscillator,

o is the range_ and

Tg is the time associated with the center of the range gate.

It will be noted that the two times and the range in the above equation are

related as follows:

2c

_t " _g " T

The integral over range may be broken up into a sum of integrals over

small segments. Later it will be convenient to make each of these segments

correspond to a range increment equivalent to the time interval of the range

gate. The resulting equation is shown here:

;, ( ) C dp drg -- = T AR hvBT dp

SNRm :0 - _ - _-

where tg is the time associated with the center of the range gate, and

R is the range associated with the center of the range increment.

One may then conveniently define the average energy as follows:

T AR

- -_ - -f--

11

(2)

(3)

(4)
mm_

and a weighted average signal-to-noise ratio contribution from the range R as;

T z_R hv BT do

T

dodTg (5)

With this definition then, the measured signal-to-noise ratio is related to the

signal-to-noise ratio contributions by the following equation,

SNRm : _ _ SN---Rc(Rn)

n=O

(6)

This equation relates the measured signal-to-noise ratio in a particular range

gate to the contributions from all different ranges, .weighted with the appropriate

transmitter energy. It may be expressed in matrix form as follows:

: E _ (7)

In this case, _ is a column matrix in which each element is the signal-to-noise

ratio contribution for a particular interval, starting with the closest and

con:inuing to the furthest. Likewise, M is a column matrix whose elements are the

measured signal-to-noise ratios in each of the range gates sequentially. The

matrix _ consists of the elements E/E. Each of these elements is defined as shown

below:

mi = SN---R m (tg = iat)

-- C_t

cj : SNRc R = j T

eij

2.1.5 CONVOLUTION

The simple expression developed in the above section suggests the approach

of inverting the matrix _, thereby solving for the SNR contributions in terms

of the measured values;

(8)

12
It can be shown that this is mathematically equivalent to the process of deconvolution, which is often accomplished by taking the Fourier transform of the measured

data and that of the convolving function, dividing the former by the latter, and

taking the inverse Fourier transform. This provides an extremely straightforward

method for extracting information where the intensity of a signal is a convolution

along the line of sight of the desired function and the transmitter energy time

history. All that is necessary is to calculate the matrix elements of _ from the

known transmitter time history. The resulting matrix may then be inverted and

used to convert any measured data set to the desired output.

In the case of the Doppler lidar, the convolution process applies to the

signals obtained at each Doppler frequency. In the present system, complete

spectral data are not available. The signal processor examines the spectrum

which arises from the convolutions described above, and extracts the amplitude

and Doppler frequency associated with the spectral peak. Thus, no information

is available concerning the amplitude of frequencies other than that associated

• with the peak. One exception which will prove useful later on is the fact that

it is known that all of these amplitudes must be less than or equal to the peak

one.

This fact may be applied in the following way. The matrix of measured

data, _for a specified Doppler frequency may be divided into two parts: the

known part and the unknown part. The known part, _k, consists of elements whose

value is equal to the measured amplitude in just those range gates in which the

Doppler velocity ,nder consideration is the one actually measured. The remaining elements are all zero. Conversely, the unknown part, _u, consists of all

zeros where the matrix _k has non-zero values, and vice versa. The remaining

question is what values to use for these non-zero elements of _u- We will

examine these in terms of their effect on the desired output. It is known that

all of these non-zero elements must be non-negative since they represent

measurements of energy in the receiver, and it is also known that the elements

of _-Imay be either positive or negative. Thus the effect of an element of Mu

on an element of the output, C,may be to increase it or decrease it. The maximum

13
valueof anelementof Cwill beachievedwhenMuhaslargepositivevaluesin just

thosecaseswheretheywill bemultipliedbypositiveelementsof _, andzero

-elsewhere.Ofcourse,themaximumvaluewhichanelementof Mumayhaveis

simplythemeasuredsignalin thecorrespondingrangegate,sinceif it were

anyhigher,it wouldbecomethenewpeakin thespectrum.Thisconditionmaybe

simulatedbyextractingfrom_-1thepositiveelements,settingthenegative

elementso zero,in a newmatrix_1. Themaximumvaluewhichanelementof

mayassumeis thenobtainedbyaddingthevaluecalculatedbythis matrixand

theunknownmeasurements to calculatewiththecompleteE°1 matrixandtheknown

elements;

CT: _-1Mk+ _I Mu (IO)

Likewise, the maximum value of an element of C is achieved when the unknown

data points are at their maximum value in just those cases where they will be

multiplied by negative elements of _-1. This may be achieved mathematically in an

analagous fashion to Equation 11, with the following results:

CN = _-1Mk " _i I Mu (11)

Having performed the calculations indicated by Equations 9, 10 and 11, one

obtains three values of the signal contribution for each velocity and each

range gate. Comparisons among these values may be expected to yield a best

estimate of the velocity at each range, along with at least a qualitative

evaluation of its validity.

2.1.6 TE_" _ESULTS

The pr:=?_ures described above have been implemented on a few sets c- Jata

from the 1984 Severe Storms Flight Test. Figure 2 shows the time history of

the transmitter pulse. For mathematical modeling, the time history has been

broken into four segments: the pre-pulse segment, the pulse, the tail, and

the ringing. The energy in the time history in various times is given by

14
pre-pulse EE = 10-0"9I _tt + I) -78Us<t <0

pulse E - I tt = 0

- 10-0.26 tt = T

tail E

- I0-1.26 e - (tt - 3/29 us) 0 < tt

ringing E

1⁄2 cos [_.1_8 2_ us (tt . T)] + I

(12)

and is computed by the FORTRAN function shown in Attachment I.

The deconvolution process is shown in Attachment 2. A portion of transformation,

[, and its inverse are shown in Figure 6. This figure shows in each case a 50 x 75

segment of the 90 x 90 matrix, with the value of the matrix element encoded in the

gray shade. It should be noted that in the display of the matrix itself, all values

shown are positive while in the display of the inverse, both positive and negative

values are shown.

A set of data which included a measurement of Mr. Shasta was used to evaluate

the deconvolution procedure. To account for difficulties in measuring the details

of the ringing, a variable phase was included in the cosine term (Equation 12), and

different values of phase were tried as shown in Figure 7. In each segment of the

figure, the top curve illustrates the time history of the transmitter pulse which

was assumed, the middle curve shows the measured signal as a function of range,

and the bottom curve shows the result of the deconvolution. Note that an arbitrary

time offset has been applied to the top curve. It is interesting to note that no

significant variations seem to exist among the six figures shown. To show this

in greater detail, three parameters of each figure were plotted as shown in Figure 8.

The variations among the different phases are small, and it appears that the best

results are obtained at zero phase. In addition to the strong peak in amplitude

indicating a return from the mountain at slightly less than 10 km, there is a

smaller signal at close range, which may be atmospheric aerosol blown from the

mountain into the beam, since the measurement was made slightly downwind of the

mountain. After the mountain, a ringing sigr_al still exists, since the deconvolution was apparently not accurate enough to remove this completely.

15
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Figure 7. Hr. Shasta Neasurements

17
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The above example was particularly simple, since the velocity measurements were

all nearly the same in a single deconvolution effort. To illustrate a more complicated example, typical of those expected in many of the interesting flow fields,

a data set was chosen in which there was a distribution of velocities. In the set

selected, most of the velocities did cluster around zero, -1, and +I meters per

second. In this case, Equations 9, 10, and 11 were all plotted in Figure 9. It

is reasonably convincing from this figure that a velocity of zero meters per

second existed in a region between about 6 and 9 km. Similar plots were constructed

for the other two velocities. In addition, one other case needed to be considered:

if there existed a velocity at which there was a significant spectral peak which

remained just below the measured one at all ranges, it would be possible for this

velocity never to appear in the deconvolution process. Thus, one case was run

with Bk : _" These results are shown in Figure 10. In principle then, it is

possible that the correct velocity for each range gate is never observed. However,

one can make convincing continuity arguments that this situation is extremely

unlikely. To better illustrate the partial deconvolution process in the case of

multiple velocities along a given line of sight, Figure 11 shows several reconstructed spectra from the range sample shown in the previous two figures. Each

figure shows four spectra. The top line, which is dotted, shows the peak of the

envelope, indicating the highest peak which could possibly exist in the spectrum.

The remaining three lines show from top to bottom the maximum expected and

minimum signal at each velocity at the range written on the spectrum. At 7.5 km the

velocity of 0 meters per second is very believable, due to the peak located there

in both the minimum and expected spectrum. A similar, but slightly less convincing,

situation exists at I meter per second at 6 km and again at -1 meter per second

at 9 km. At 19.5 km, all the spectra are considerably lower than tFey were in the

previous cases, and it is unlikely that it is possible to make a valid velocity

estimate.

2.2 MODULATOR REFURBISHMENT

Upon receiving the two modul.ators back from the Marshall Space Flight Center, a

number of tests were completed to recharacterize them. In the present Severe

Storms system, the first modulator acts as an optical switch and the second as

a "tail biter." During the last field test, the "tail biter" was electrically

damaged, thus the need arose to reevaluate the modulator performance.

19
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Figure g. Three Convolutions at Zero Velocity

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The extinction ratio and transmission of the modulators in tandem and also

separately were measured. In addition to this, an infrared transmission scan

wasdone.

Upon completion of these experiments, the modulators were tested for optical

ringing and the optical pulse height to optical ringing ratio was determined.

The data from these two experiments indicated that two new crystals and modulator

housings were needed. The crystals were ordered in April and a mid-November

(previously mid-June) delivery is expected. The modulator housings were

redesigned and fabricated to optical ringing. The design implemented has been

successfully used on other Raytheon programs. Since the new crystals had such a

long lead time, the original switching modulator was reworked (end faces repolished).

This reworked crystal has been mounted in the new modulator housing and similar

tests have been completed. The results of these tests will be summarized

and forwarded to MSFC shortly.

2.3 ISOLATOR REFURBISHMENT

New indium antimonide was ordered and received in July. These wafers were

polished by Cominco rather than the Research Division at Raytheon because they

claimed they could do the work at minimal cost. The material was sliced from the

original crystal grown in 1977. Examination of the received wafers indicated that

Cominco did not have the skill in polishing as claimed. In addition, there is a

surface mark on each wafer on the same face. (Crystals have an antimenide side and

an indium side.) The surface mark is a sign of a material inclusion that propagates

throughthe crystal and is therefore found in each slice. Inclusions can have a

bad effect on the optical wave front as it passes through the crystal acting in

effect as a lens since the index will be different than surrounding material.

Tests are underway to examine the wafers at 10.6 IJm.

Old wafer stock, not yet polished, will be polished at Research as soon as

blocking stock can be located. New stock will be ordered from Cominco in the

raw cut state only.

23
2.4 IMPROVED CALIBRATION SETUP

There are several problems with the existing internal calibration equipment.

The signal-to-noise ratio (SNR) is very sensitive to the tolerance of the wheel

placement due to the acute focusing of the present lens. In addition, the wheeldriving motor produces a non-optimum Doppler frequency, and the SNR exceeds the

dynamic range of the processor.

An existing 5.5X expander used in reverse would shrink the output beam substantially to give a more narrow focal point.

The wheel will continue to be placed at an angle of incidence of 45 ° due to

the mass of accumulated data already processed at that angle.

The motor, which drives the wheel, should be upgraded to raise the Doppler

frequency (fD) above 3 MHz. A 3.6K rpm motor would produce fD = 4.087 MHz.

With a speed of 3.6K rpm, a beam size at the target of 4 mm would be

required to produce a passband of 100 kHz.

It has been determined that the optimum situation would produce a spot less

than i mm on the wheel. Therefore, the length of time a particle is in the

beam comes into effect to determine the passband. A particle on the disc (at

the operating radius of 8.13 cm) will take 4.5 x 10-5 s to pass through the

beam, which results in a 22-kHz passband.

2.4.1 RESULTS AND DISCUSSION

A diagram of the modification is depicted in Figure 12, showing the

proposed 5.5X expander in reverse and dimensions of the system.

The existing 5.5X expander design is recon_ended to be manufactured, and a

3.6K rpm closed motor should be purchased.

3. PLANS

A new beam expander will be designed for the local oscillator. A cooperative

effort with National Severe Storms Laboratory will begin on evaluating the

velocity accuracy.

24
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At this point, all possible testing and fabrication have been completed.

As soon as the new crystals arrive, they will be mounted in their respective

modulator housings and individual and tandem testing will be finished.

26
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o.)

7:; :.

3O