\

''"?EAU 0» ,**

NBS TECHNICAL NOTE 1031

U.S. DEPARTMENT OF COMMERCE /National Bureau of Standards

The Use of LEDs to Simulate

Weak Yag-Laser Beams

NO. 1031

1981
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or 9tAin>AB»8

UBllAItT

The Use of LEDs to Simulate '"''« ^^^ Weak Yag-Laser Beams

ck(c>o

no, IClf

N6^ rtck^cQu( nok^ c.->-

M. Young

Electromagnetic Technology Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

*«.*' \

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued January 1981
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 1031

Nat. Bur. Stand. (U.S.), Tech. Note 1031, 48 pages (January 1981

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1981 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $2.50 (Add 25 percent for other than U.S. mailing)
f CONTENTS

PAGE

Abstract I iv

Apparatus and Procedures 2

Wave! ength 7

Beam Divergence 12

Pul se Durati on and Shape 21

Energy Density and Uniformity 21

Summary and Concl usi ons 25

References 26

Appendi x A 27

Appendi x B 30

Appendix C 33

Appendi x D 36

Appendix E 39

Appendi x F 41

m
THE USE OF LEDs TO SIMULATE WEAK YAG-LASER BEAMS

M. Young

Electromagnetic Technology Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Abstract

The purpose of this report is to determine whether and under

what conditions a light-emitting diode may be used to simulate a weak YAG-laser beam that has been scattered by a distant reflecting object. By examining the differences between laser radiation

and LED radiation, we conclude that there is no theoretical reason that a LED may not be used in place of the laser beam.

Key words: Laser simulator; light-emitting diodes; YAG laser.

IV
THE USE OF LEDs TO SIMULATE WEAK YAG-LASER BEAMS

1 The purpose of this report is to determine the conditions under which a light-emitting diode (LED) may be used to simulate a weak laser pulse at the

wavelength of 1064 nm. The pulse is presumed to have originated from the diffuse scattering of a laser beam off a distant object. We seek to determine

the feasibility of testing the receiver of such a pulse with the suitably collimated and filtered radiation of a 1060-nm LED.

Much of the report is theoretical; the remainder is either experimental

or supported by experimental evidence. Because of the organization of the

document, theoretical and experimental considerations are not divided into

separate sections; rather, we take the approach outlined below.

We begin by asking the question. What are the potential differences between laser radiation and LED radiation? The laser radiation in question is

presumed to be Nd:YAG radiation that has been scattered from a distant object. The LED radiation is presumed to have originated from one of several

(nominally) 1060-nm LEDs that are on the market.

To answer the question, we have compiled a list of parameters that will

have to be examined. We have tried to make the list as exhaustive as possible, even though in some areas potential problems may be dismissed out of

hand. The list is presented as Table 1. Other ways of organizing the list

are possible; this organization best suits our needs.

Table 1.

Potential Areas of Difficulty

1. Wavelength.

a. Wavelength of maximum power.

i. Detector responsivity vs. wavelength.

b. Linewidth.

i. As it relates to a. ii. Coherence length.

c. Chirping of LED.
2. Beam divergence.

a. Degree of collimation of simulator, compared with laser return.

b. Spatial coherence.

3. Pulse duration and shape.

4. Energy density over aperture.

a. Uniformity over aperture.

b. Pulse-to-pulse energy.

Apparatus and Procedures

describe

Before

the

going

experimental

on to discuss

apparatus.

the entries in Table 1 in detail, we mustM

We obtained six LEDs whose wavelength was nominally 1060 nm. We excited

the LEDs with a signal generator that could provide electrical pulses up to

2 A and as short as 20 ns. The circuit is shown in Fig. 1. The diode provides protection for the LED in case of a strong, negative reflection. The

series resistor provides an impedance match to the 50-fi coaxial cable; its

value is chosen experimentally by time domain reflectometry.

A microwave tee with a 270-n resistor is used to sample the electrical

pulse in the coaxial cable. We use enough cable between the LED and the

generator to provide a 35-ns round- trip delay and operate the generator at the

20-ns setting. We use a sampling oscilloscope to observe the direct and

reflected waveforms as they pass the tee. Following [1], we adjust the value

of the series resistor until the waveform shows slight undershoot; when possible, we also ensure that none of the secondary oscillations becomes positive, because this will cause a small, secondary optical pulse. Figure Z shows the effect of changing the series resistor on the electrical waveform of

a particular LED.* The data were taken with the horizontal and vertical outputs of the sampling oscilloscope connected to an xy recorder; the vertical

output was filtered with a capacitor to reduce noise (more on this later).

In principle, the effective impedance of the LED and of the diode are functions of peak current and waveform. However, we have found that slight

*The use of product names is intended for the convenience of the reader and

does not imply endorsement by the National Bureau of Standards. Products of

other manufacturers may work as well or better.
Pulse

Generator

270 a W^AV

IN 4153

20-dB

Attenuator

Sampling

Oscilloscope

X out

Nj/

Y out

Ni/

To XY Recorder

Circuit for driving 1060-nm LED and monitoring direct and reflected current

waveforms.
25 ns

Figure 2a. Examination of direct and reflected current waveforms as function of serie*

resistance.
Optical

25 ns

Electrical

e^iure 2b. Optical pulse emitted when LED is driven by current waveform shown. Diode is a GAL 100, with a 43-fi series resistor and approximately 1-A peak current.

II
+ 300 V

100 kQ

1060 nm

0.01 yF

S I! X

C30817

\[

1 yF

1 yF

TIED 150

10 kfi

Sampling

Oscilloscope

X Out Y Out

To XY Recorder

Figure 3. Avalanche photodiode and associated electronics.
changes of the peak current are not serious. We matched the impedance of the

system at the peak current of 1 A but frequently operate satisfactorily at

2 A. To detect the radiation, we use an avalanche photodiode, usually followed

by a transimpedance amplifier and sometimes by a radio-frequency amplifier as well. The circuit is shown in Fig. 3. As before, the waveform is detected by

the sampling oscilloscope and transcribed by the xy recorder.

For many experiments, we wanted to measure the optical power at a given

time (such as the peak of the pulse) as a function of some parameter such as wavelength or source or detector position. For this purpose, we fashioned a mechanical -to-electrical transducer and used the transducer output to drive

the horizontal motion of the xy recorder. For the vertical motion, we set the

sampling oscilloscope on "manual" and set the display at a fixed time; we use

the output of the oscilloscope to drive the vertical amplifier of the

recorder.

The sampling oscilloscope displays about 5 mV of noise, peak to peak;

when we use the rf amplifier, it adds another 5 mV of noise. Many times, this

results in a signal-to-noise ratio no better than 3 or 5. In part to reduce

the effect of this noise, we record our waveforms with the xy recorder instead

of the more-common oscilloscope photography. By scanning sufficiently slowly

and integrating with a capacitor, we perform an analog average of the noise

and improve the signal-to-noise ratio by an order of magnitude or more.

We will describe further details of the experiments as we need them. The

rest of the report is organized parallel to Table 1.

Wavelength

The YAG laser emits radiation at the wavelength of 1064 nm; its linewidth

is of the order of 0.5 nm. The LEDs, on the other hand, display a peak wavelength in the neighborhood of 1060 nm and a linewidth of about 50 nm. In

addition, the peak wavelength depends on temperature, so there is the possibility that the spectrum will drift during the course of the pulse (this is

known as "chirping").

To assess these problems, we first calibrated a V4-meter grating mono- chromator with a continuous-wave YAG laser. We excited the LEDs with 2-A,

20-ns pulses and observed the spectrum at various times during the pulses.
For this purpose, we set the oscilloscope on "manual," as described above, and

electrically connected the wavelength drive of the monochromator with the

horizontal amplifier of the recorder.

Figure 4 shows some spectra obtained with one of the LEDs. In general,

the wavelength of maximum radiance is not 1064 nm, but is more nearly 1050 in

most cases. The linewidth and wavelength of maximum for all six LEDs are com- piled in Table 2 and compared with the manufacturers' specifications.

Table 2.

Spectral Data on LEDs

Wavelength

of maximum (nm)

spec actual^

Linewidth (nm)

spec actual

P(1064)/

p

'^max

C30116/F #1 1030-1090^ 1047 60 45 0.72

C30116/F #3 II 11 1045 II 42 0.56

GAL 100 1050-1065^ 1050 55 50 0.85

GAL 101 #1 1050-10652 1042 II 51 0.57

GAL 101 #2 II II 1045 II 52 0.73

Power at 2-A

drive (mW)

spec

^ At 27*^0 ^ At 25'*C

2 At 25*C ^ Into F/1 cone

Let us assume for the moment that one of the LEDs is to be calibrated

with an instrument that contains a silicon detector. The detector's responsivity has been calibrated with a YAG laser at the wavelength of 1064 nm. A

check of several manufacturers' specifications shows that the responsivity of

the detectors varies with wavelength by 1 to 2 percent per nanometer. Therefore, the calibration will be in error by about 10 percent if the maximum

wavelength of the LED is in the range of 1050 to 1055 nm. Possibly this will

not be a serious error. More important, however, is the problem of using the LED with an instrument that contains a narrowband filter centered about 1064 nm. Let us assume

that the filter has a bandwidth of 10 nm. The system is designed to detect

radiation whose linewidth is substantially less than 10 nm; thus, to calibrate

IT?
I

1000 1050 1100 nm

ure 4. Spectra of C30116/F #1. 1—beginning of 1-ys pulse; 2--end of 1-ys pulse;

3--second half-power point of 20-ns pulse; 4--first half-power point of 20-ns

pulse; 5--peak of 20-ns pulse. Peak current was 2 A and repetition frequency

was 1 kHz. Vertical scales are not necessarily the same.
the system directly with a LED, the LED will have to be filtered to 0.5 nm o so. Most of the radiation from the LED is therefore discarded (see Appendix

A).

If the accuracy required is not too great, it may be desirable to use the

LED unfiltered. Its spectrum must be measured and the transmittance through

the receiver's filter calculated. Appendix A shows how to estimate this

transmittance for the purpose of initial design. The estimate is reasonably

accurate, provided that the linewidth of the LED greatly exceed the bandwidth

of the filter.

A third approach is to filter the LED radiation with a filter that is

identical to the filter inside the receiver. The calibration of the emitter

is performed on the filtered radiation; there is no need to measure the spectrum. Twenty to fifty times more power will be available than with the

narrowband filter, but the measurement of the receiver's responsivity must be

performed with care. Appendix A shows how to calculate the transmittance of a filter when the

spectrum of the radiation is identical to the transmittance curve of the

filter. When the spectrum can be approximated adequately by a Gaussian function, the overall transmittance of the filter is 0.35 times the maximum transmittance Tq. If the filters are not precisely identical or if the Gaussian

approximation is inadequate, then the factor will differ from 0.35. The

transmittance is not, in any case, T^ and must be calculated correctly if the

simulator is to be calibrated with a filter that is similar to the filter in

the instrument.

In cases where energy is limited, we favor the last approach because it

makes relatively efficient use of the total LED radiation and because the

required calculation does not depend on a measurement of the spectrum of each

LED. When energy is not limited, the narrow-band filter is appropriate.

The linewidth of a source also determines the temporal coherence of the

radiation. The linewidth of the YAG laser is about 100 times less than that

of the LED; its coherence length is therefore 100 times greater. It may be

argued that the higher coherence of the laser will cause effects that will not

be seen when the LED is used as a source.

The coherence length of a source is equal to 1/2ttAv, where av is the

linewidth in the frequency domain [2]. The coherence length of the YAG laser

is about 0.5 mm. There should be no problem resulting from coherence unless

Id
the system contains two surfaces that are precisely parallel and well under a millimeter apart. The filtered LED radiation will display a greater linewidth

than the laser; temporal coherence will therefore be less a factor.

Finally, we address the problem of chirping. Chirping could result from

rapid heating of the diode during the current pulse (see Table 3). To determine whether the wavelength of maximum radiance shifts during the pulse, we recorded the spectra of several of the LEDs at different times during the

pulse. For example. Fig. 4 shows the spectra at the first half-power point,

the peak and the second half-power point of a 2-A, 20-ns pulse. Apart from

power, the spectra are not distinguishable.

Table 3

Wavelength of "Typical" LED vs. Temperature*

Temperature (K) Wavelength (nm)

120 1004

140 1009.5

160 1014

180 1019

300 1050

*These data and certain others courtesy of Rudy Garza, Plessey Optoelectronics

and Microwave Ltd.

Further to ensure that chirping would not be a problem, we lengthened the

pulses to 1 ys and measured the soectra at the beginning and end of the

pulses. We thereby established an upper limit of ~ 1 nm/ys to the rate of

wavelength drift of the LEDs (GAL 101s) with the highest current density.

This is negligible compared with the ~ 50-nm spectral width of the source. We

therefore conclude that chirping will not be a problem at least up to the peak

current of 2 A. If the pulse duration is restricted to < 100 ns, we speculate

that chirping will be negligible up to the maximum rated current of 10 A.

11
Beam Divergence

If a source is placed precisely at the focal point of a diffractionlimited lens, the beam refracted by the lens will be colli mated but will still

exhibit a small divergence. The divergence will result either from diffraction or from the finite size of the source. In either case, we refer to this

residual divergence as "the beam divergence"; it is to be distinguished from

the divergence of a beam that is not as well collimated as possible.

Beam divergence in the LED simulator is important if the receiver to be

tested is spatially filtered to limit the field of view to a certain angle.

If this is the case, then the LED radiation will have to be collimated and its

beam divergence restricted to less than the field of view of the receiver.

To pursue this investigation further, we describe a "typical" system that

will serve as a paradigm for all practical systems (see Table 4). Consider a laser transmitter that projects a beam with (full -angle) divergence 0.5 mrad

onto a diffusely scattering object 10 km distant. The receiver that detects

the scattered light is alongside the transmitter and is therefore also 10 km

distant from the scatterer. (We do not discuss here whether or not the laser

radiation can be detected in the presence of a daytime background.) A detector is located at the focal plane of the objective lens associated with the

receiver.

Table 4

"Typical" System

Wavelength 1064 nm Linewidth 0.5 nm Beam divergence (full angle) 0.5 mrad

Energy per pulse 0.1 J Duration 50 ns Range 10 km

Receiver entrance pupil diameter 10 cm Receiver linewidth 10 nm

Figure 5 shows the geometry, il is the range and a is the divergence of

the transmitter. The size of the spot projected onto the diffuser is
e %

Figure 5. Geometry of laser beam scattered by distant diffuser.

13
Fiqure 6. Divergence of beam colli mated by lens with finite source,

14
375 ym

500 m

Figure 7a. Near-field scan of C30116/F #3.

15
250 ym

Figure 7b. Near-field scan of GAL 100.

16
500 vjm

Figure 7c. Near-field scan of GAL 101 #2,

17
therefore £a. To detect all the radiation scattered into its entrance pupil,

the receiver must have a field of view at least equal to the diameter of the

illuminated spot divided by the range. This is just equal to the divergence

of the transmitter, or 0.5 mrad. We shall therefore require that the LED

radiation be collimated and its divergence restricted to less than 0.5 mrad.

The beam divergence is determined from the geometry of the LED and the

collimatinq lens or mirror. Figure 6 shows that the beam divergence is equal

to the diameter of the LED divided by the focal length of the lens. For

example, a 0.1-mm LED (such as a GAL 101) will give a beam divergence of 0.2

mrad when collimated by a 50-cm lens. In addition. Appendix B shows how to

calculate the acceptable amount of focus error for given geometry.

The beam divergence is more easily calculated than measured directly.

However, it is instructive to scan the near-field radiation pattern of the

LEDs. We have performed this scan by fixing the LEDs to a translation

stage. The stage is connected (with the position transducer) to the horizontal amplifier of the xy recorder. The image of the LED is projected with a lOX microscope objective onto the plane of a detector that is considerably

smaller than the image. Figure 7 shows the results of some near-field scans;

Table 5 relates the manufacturers' specifications with the measured diameters

of the radiation patterns.

Table 5 Dimensions of LEDs

Spec Measured luminous

i]M) diameter (ym)

450 1700

450 1600

C30116/F #1

C30116/F #3

GAL 100 400 400

GAL 101 #1 100 550*

GAL 101 #2 100 560*

'Apparent diameter, seen through ruby lens and thin layer of GaAs.

18
The C30116/FS appear considerably larqer than the manufacturer's claim.

In addition, most of the radiation emanates from a ring around the outside of

the pattern. We inspected the LEDs with a microscope and, through the microscope, with an infrared viewer. Although they are classified as surface emitters, they clearly emit a large fraction of their radiation through the edges

of the chip; this radiation is reflected from the rounded sides of the well in

which the chips appear to sit. Most of the radiation that reaches the outside

appears to be such reflected radiation. This has the effect of making the

effective source larger than the LED itself. (The manufacturer's specification evidently refers to the size of the chip.)

The GAL 101s likewise appear considerably larger than the lOO-ym emitting

area claimed by the manufacturer. According to the manufacturer, the junction

of the LED lies 20-45 ym below the surface of the chip. A hemispherical ruby

lens with ~ 400 \m diameter is contacted to the chip. This optical system

produces a virtual image of the emitter at very nearly the location of the

emitter. The magnification of this optical system is about 1.8 (see Appendix

C); the scan reveals a source several times larger than 180 ym.

We examined these LEDs as well with the microscope and the infrared

viewer. Our examination verified that the apparent source diameter is several

times larger than the virtual image of the emitter (which could be seen as a small circular area behind the hemispherical lens). Because we do not know

the structure in detail, we cannot account for the apparent size of the

source.The ruby lens probably increases the irradiance in the forward direction

by roughly the amount estimated in Appendix C. However, the apparent radiance

of the GAL 101s is substantially less than what would be calculated on the

basis of a 180-ym emitter. If a source whose diameter is truly 100 ym is

required, then it may be possible to obtain one by using this LED without the

ruby lens. (We obtained one LED without the lens; it broke after being

mounted and could not be replaced in time for this report.)

The nonuniformity of the near-field scans of the LEDs is acceptable, provided that the overall beam divergence be sufficiently small; that is, provided that the focal length of the lens times the acceptable beam divergence

exceed the total luminous diameter of the LED. The nonuniform near field will

not affect the uniformity of the beam across the surface of the collimating

lens.

19
The beam divergence will be equal to that calculated provided that the

collimatinq lens be sufficiently aberration free. The properties of the lens

may be calculated by a ray trace if necessary; however, third-order aberration

theory is sufficiently precise. When one conjugate is located at infinity,

the optimum lens shape is very nearly planoconvex. Because planoconvex lenses

are readily available, we restrict ourselves to this type. Appendix D shows

how to calculate the third-order aberrations of a planoconvex lens oriented

with the curved side toward the infinite conjugate. The lens will be diffraction limited if the overall aberration is less than the Airy-disk radius; it

will display acceptable quality if the aberration is less than the size of the

emitter. Further details are left to the appendix.

The size and range of the illuminated diffuser also influence the degree

of spatial coherence of the radiation incident upon the receiver. If a distant, diffuse object is illuminated with spatially coherent radiation, the

radiation scattered onto a plane will exhibit the random interference pattern

called "speckle." If the plane is located in the far field of the scatterer,

then the speckle size is about 1.6 X£/D, where i is the range and D is the

diameter of the scatterer [2]. The speckle area is also equal to the coherence area in the observation plane.

In our case, the far-field distance is hundreds of kilometers from the

illuminated patch. However, the speckle size is still approximately that

stated above, provided only that many points on the scatterer contribute to

the amplitude at any point in the observation plane [3]; this is nearly always

the case. We further assume that the coherence area remains equal to the

speckle size when in the near field.

We assume the receiver to have a 10-cm-diameter lens. If the receiver is

located 10 km from the scatterer, then about 900 speckles fall onto the lens.

Because tfie number is so large, the light may be assumed to be completely

incoherent.

Except in the special case where the LED is smaller than the diffraction

limit of the collimating lens, the emission from the simulator also is spatially incoherent. Therefore, coherence presents no obstacle to using the LED

to simulate the laser return.

Incidentally, the speckle pattern has another effect. The number of

bright speckles inside the entrance puDil of the receiver lens is about 450

(half of 900). As a result, the relative fluctuation from shot to shot will

20
be 1//450, or about 5% [4]. Fluctuations with this origin will not exist with

the LED source.

Pulse Duration and Shape

The pulse emitted by a 0-switched YAG laser may have a duration from 10

ns to 50 ns or more; often the risetime is substantially shorter than the

decay time. We have driven the LEDs with electrical pulses with durations as short as 20 ns and as long as 1 ys. The electrical pulses were symmetric, and

the optical pulses were virtually indistinguishable.

The LED manufacturers claim rise and decay times less than 10 ns; this is

consistent with our observations. We have made no attempt to determine the

ultimate performance of the LEDs.

The LED pulses could, no doubt, be tailored to match the laser pulses,

but we cannot foresee any purposes for which this would be desirable. We assume that the receivers would in general be energy detectors; that is, they

respond to the energy of the pulse and ignore the waveform. In that case, any

LED pulses with the right energy and roughly the right duration would suffice

for calibrating receivers. We have easily obtained 20-ns optical pulses, and

Franzen and Day in our laboratory have shown how to generate 2.5-ns pulses

with similar LEDs [1]. We therefore do not believe that the time-domain properties of the LED pulses will be a hindrance.

Energy Density and Uniformity

Here we address the problem of generating a collimated beam with sufficient intensity and uniformity over a 10-cm diameter. We show in Appendix E that we can expect a total of no more than 10"-^^ J to be collected by the

10-cm objective of the system described in Table 4. We also estimate in that

appendix that about that amount of unfiltered energy can be provided by the

LEDs with drive currents in excess of 2 A. To assess the uniformity of the beam across a wide aperture, we roughly

collimated the emission from the diodes with a lens whose focal length was about 20 cm and diameter about 10 cm. We pulsed the LEDs and scanned the

detector across the aperture of the lens. This procedure does not measure the

radiation pattern as a function of angle; for that, we would have to restrict

21

urn
the detector to a circle centered about the LED. Rather, it measures the

more-relevant (for us) irradiance across the exit pupil of the lens.

Figure 8 shows the results of some scans across the F/2 lens. The LEDs

that do not use lenses display approximately uniform irradiance across most of

the F/2 aperture. The LEDs with the ruby lenses are uniform to ± 5% over about an F/4 aperture.

We also used a uniform large-area silicon detector to measure the

approximate power each LED radiated into an F/8 cone. These results are tabulated in Table 6, column 1. We then calculated the approximate power radiated

into cones with different F numbers; these calculations are tabulated in the

remaining columns of Table 6.

Table 6

Total Energy (lO"-'-^ J) Radiated Into Various Cones*

F/8 F/4 F/10 F/20

1.5 5.8 0.93 0.23

1.4 5.7 0.91 0.23

1.4 5.5 0.88 0.22

1.7 6.7 1.1 0.27

3.1 12.0 2.0 0.50

C30116/F #1

C30116/F #3

GAL 100

GAL 101 #1

GAL 101 #2

*For 20-ns pulses, 1-A peak current. To convert to other F numbers, multiply

the figures in column 1 by {8/F number)^. To convert to other pulse durations, multiply by (duration/20 ns). To convert to other currents, multiply

by (current/1 A).

It is possible to radiate a few times lO"-'-^ J into an F/8 cone using any

of the LEDs with a drive current of 1 A and a duration of 20 ns. This may be

increased by an order of magnitude or more by increasing the current to 10 A

and the duration beyond 20 ns.

22
C30n6/F #1

C30116/F #3

F/8

F/4

F/2

Figure 8a. Exit-pupil scan of three LEDs.

^S
GAL 101 #1

GAL 101 #2

'-V.^V.A^

F/8

F/4

F/2

Figure 8b. Exit-pupil scans of two GAL 101s with ruby lenses.

24
If the receiver system contains a 1-nm filter with its peak at 1064 nm,

then the total energy that passes the filter will be at least two orders of

magnitude less than the energies listed in Table 6.

Summary and Conclusions

We have shown that there is in principle no reason that an LED may not be

used to simulate a diffusely reflected laser beam with certain properties.

The most-important practical problem we can foresee is generating sufficient

energy per pulse at the right wavelenath.

The detailed design of a system is well beyond the scope of this report.

However, in such a design, there will likely be compromises made between beam

divergence and energy per pulse. For example, if a comparatively large beam

divergence may be tolerated, then a relatively low F-number lens may be used

to increase the total energy that passes through an aperture with a given diameter. On the other hand, a low beam divergence will require the designer to

sacrifice energy by using a low-aperture collimating lens or a spatial filter

to reduce the apparent diameter of the source. Another decision will be whether to (spectrally) filter the LED radiation

or to measure the total energy radiated into the lens aperture and to rely on processing to calculate the responsivity of the receiver being tested.

Beyond these, we suspect that the design of a simulator system will be

comparatively straightforward if the designer adheres to the principles

described in this report.

25
References

[1] Franzen, D. L., and Day, G. W., LED source for determining optical

detector time response at 1.06 ym, Rev. Sci . Instrum. 50^, 1029-1031

(1979).

[2] Young, M., Optics and lasers, Springer-Verlag, New York, Heidelberg,

Berlin, 1977, Chap. 4.6. Young, M., et al . , J. Opt. Soc. Amer. ^, 137-8

(1970).

[3] Dainty, J. C, The statistics of speckle patterns. Sect. 2.1, in Progress

in Optics, Vol. XIV, Wolf, E., ed., North-Holland Publishing Co.,

Amsterdam, New York, Oxford, 1976.

[4] Young, M., and Lawton, R. A., Measurement of pulsed laser power, NBS

Technical Note 1010, 1979, Sect. 3.

[5] Ref. 2, Chaps. 1.2 and 2.2.

[6] Ref. 2, equation 1.17.

[7] See, e.g., an article by Smith, W. J. in The Infrared Handbook, Wolfe, W.

L. and Zissis, G. J., eds., U.S. Government Printing Office, Washington,

1978; or in Handbook of Optics, Driscoll, W. G. , ed., McGraw-Hill Book

Company, New York, 1978.

[8] Day, G. W. and Stubenrauch, C. F., Laser far-field beam-profile measurements by the focal plane technique, NBS Technical Note 1001.

[9] Ref. 2, Chap. 3.1.

26
Appendix A

Effective Transmittance of an Optical Filter

Here we wish to calculate the overall transmittance of a filter when the

filter is illuminated by a specific source. We describe the transmittance

function of the filter by the function T{x), where T has the maximum value of

Tq. The emission spectrum of the source and any additional filters that may

be placed in front of the source is described by the function S(x). For

mathematical convenience, we normalize S so that

Q S{\) dX = 1 . (AD

The power transmitted by the filter at any wavelength is equal to the

product of S and T; therefore, the net (overall) transmittance T^ of the

filter is the intearal

,

"•"f " -^0 ^^^^ ^^^^ ^^ • ^^^^

For exact calculations, the integral must be evaluated digitally after S

and T are measured. However, for many purposes, it will suffice to approximate both S and T by Gaussian functions,

S(X) = (1/AX ) exp[-T:(X-X )2/AX 2] (A3)

s s s

and

T(X) = T^ exp [-tt(X-X^)2/AX^2]^ (;^4)

where l/AX^ is a normalizing factor that satisfies Eq. (Al). The subscripts s and t refer to S and T; x^ and x^ are the wavelengths at which S and T are maximum; and AX is the full spectral width at half maximum.

Three cases are important to us. First, assume that S and T are represented by the same function; that is, X = x. and AX = ax. . The integral in

Eq. (A2) becomes for this case,

27
T^ = (T^/AX) /^ exp[-27T(X-X^)2/Ax2] dX . (A5)

The integral is readily evaluated; Eq. (A5) reduces to

T^ = 0.3S T . (A6)

i

11 When the spectrum of the source and the transmittance of the filter match, the"'

net transmittance of the filter is about one-third the maximum transmittance. bj

The second case of interest is that for which AX << ax . This approxi-

"'

mation will be appropriate when the LED radiation is to be processed with a relatively narrow-band filter. In this case, Eq. (A2) may be written as

Tf= S(X^) Q T(X) dX , (A7)

where S(x) is assumed constant over the region where T(x) is significantly

greater than 0. Using the Gaussian approximation again, we find that

T. = S(x.) T^AX. . (A8)

f tot

Equation (A8) may be written in a more convenient form. Let

F(x) = S{x) AX^ . (A9)

F(x) is simply another way of describing the spectrum of the source; when

X = Xg, F{Xg) is equal to 1. In terms of F(x),

T^ = TqF(X^) AX^/AX^ . (AlO)

Finally, when the source spectrum is significantly narrower than the

filter transmission spectrum, Eq. (A2) becomes

Tx = T(Xj r S(X) dX , (All)

t S
whence

Tf = T{X^)

The three results of this appendix are summarized in Table Al

Table Al.

Effective Transmittance of Optical Filter

AX, < AX^ T^ = T^F(X,)AX./AX^

T S f f T S

AX = AX , s'

X = X

s

T, = 0.35 T

f

AXOS> AX T = T(X ) s

29
Appendix B

Calculation of Acceptable Focus Error

In this appendix, we calculate the precision with which the LED must be

located at the focal point of the collimating lens. The calculation is

similar to other treatments of depth of focus in photography [5].

Figure Bl shows the collimator and the receiver. For the moment, the LED source is taken to be a point source. The receiver is presumed to have a field stop at the focal point F2 of the objective lens. The stoo restricts

the field of view of the instrument to the angle a. The radius of the stop

(which may be the detector itself) is therefore f'a/2. The image is located

not at F^, but at 0^; the depth of focus of the receiver is 6. Using similar

triangles, we calculate that

6 = {f^)VD. (Bl)

where 6< f2. + 6 is the acceptable amount of focus error of the receiver,

provided that the incident radiation is truly collimated.

2 Using Newton's form of the lens equation, x x' = - f , [5] we may find

the nearest object point O2 whose image will not be vignetted by the stop at

F^. This is

X2 = - D/a , (B2)

where the minus sign indicates that the point is to the left of the primary

focal point of lens 2.

Lens 1 provides a virtual object for lens 2. The virtual object is the

image of the source as seen through lens 1. If the virtual object is located

at 0^, then its image is projected to O2. The system is then on the verge of

being out of focus. We wish to calculate the source position x^ that corresponds to this virtual -object position. For this purpose, we apply Newton's

form again, with

x'l = X2 = -D/a . (B3)

30
^ \m. Simulator Receiver

Figure Bl. Geometry used for calculating acceptable focus error.

31
The result,

xi = - aflVD (B4)

indicates the acceptable amount of focus error in the collimating system, presuming that the LED is a point source. Using the parameters relevant to the

paradigmatic system of Table 4 (D = 10 cm, a= 0.5 mrad) and assuming that

f' = 200 cm, we find that the depth of field is 2 cm. The depth of field is

very nearly symmetrical about the focal point, so the tolerance is really + 2 cm. The source is in reality not a point. With a finite source, the depth of

field drops linearly to zero as the angular subtense of the source increases

from zero to a. For example, if the source subtends a/2, then the depth of

field of the collimating lens is ± 1 cm.

32
Appendix C

Paraxial Optics of a Hemispherical Lens

Figure CI (a) shows a hemispherical lens contacted to a substrate that has

a source a distance t behind it. We wish to find the image of this source and

the magnification.

To begin, we apply the "len" equation for a single spherical refracting

surface [6],

(n'/ii') - (n/£) = (n' - n)/R . (CI)

The primed symbols refer to the image space, the unprimed symbols to the object space. When n and n' are not equal, the magnification m is given by

m = (n/n') {V /l), (C2)

rather than the customary V /l.

To locate the image, we first apply Eq. (CI) to the GaAs-ruby interface,

for which R = «. The result, ii = -(n'/n)t, reduces to about t/2 when the

appropriate indices are used. (The minus sign indicates that the image is to

the left of the interface.) This is the virtual -object point for the ruby-air

interface. According to Eq. {C2), the magnification of the image is 1. We now apply the "len" equation to the second interface, with object distance l^ = ii|. The result, Zz = - 432 ym, locates the virtual image of the

original object. The magnification of this stage is (n/n') ()l'/^) = LB. The

magnification is mainly the result of the fact that the object and image

spaces have different indices of refraction and is very nearly the ratio of

the indices. As long as t is small compared with R, object and image will lie

relatively close together; magnification will vary only slightly with changes

of the ratio t/R and will be eaual to (n/n') when t=0.

We now ask. How is the on-axis irradiance influenced by the presence of

the ruby lens? As Fig. Cl(b) suggests, the lens brings about an increase of

irradiance as the result of two factors: reduced reflection loss and

decreased spreading of the beam refracted at the surface of the GaAs.

33
Figure Cla. Hemispherical lens contacted to a substrate with source a depth t

inside substrate.

n=3.3

T = 71% T = 84%

3.3 i

Figure Clb. Refraction by substrate-air interface without (left) and with

(right) ruby lens.

34
Near to normal incidence, the reflectance at an interface is given by the

familiar formula,

R = (n-l)2/(n+l)2 ; (C3)

the pertinent indices are 3.3 and 1.7 for GaAs and ruby. The reflectance of a Ga As-air interface is 0.29; the transmittance is therefore 0.71.

Consequently, if a ray originates inside the GaAs, only 71% of the power is

transmitted across the interface into the air.

Suppose, however, that a ruby lens is contacted very efficiently to the

GaAs, as in Fig. Cl(b). (We presume that the index of the cement is close to

that of the ruby.) Then the transmittances of the two successive interfaces

are 0.90 and 0.93; the overall transmittance is 0.84. The gain from reduced

reflectance is 0.84/0.71 = 1.18.

Now suppose that a ray crosses the surface of the GaAs with angle of

incidence i, which is small. The angle of refraction is 3.3i when the ruby

lens is not present, but it is reduced to (3.3/1.7)i when the ruby lens is

added. (Because the lens is hemispherical, the angle of incidence at the

ruby-air interface is 0.) Thus, a narrow cone directed at the surface of the

GaAs is spread into a larger angle when the lens is absent than when it is

present. Because of the two-dimensional symmetry, this translates into an increase of irradiance of 1.7^ as the result of the concentrating effect of

the ruby lens.

The total gain resulting from the presence of the lens is the product

1.7^ X 1.18, or about 3.5. This is a power or irradiance gain and not a radiance gain. Because of the magnifying effect of the ruby lens, the in- crease of source radiance cannot exceed what is gained by reduced reflectance,

or about 1.2. If the ruby lens is responsible in some way for the unexpectedly large source diameter noted in the main text, then radiance is actually

lost rather than increased.

35
Appendix D

Aberrations of a Planoconvex Lens

The divergence of the collimated radiation will equal the angular subtense of the LED provided that the aberrations of the lens are kept within

certain limits. If space and power are not factors, then the collimator may

be a single-element lens with a long focal length and relatively low aperture. (The same is true of the receiver.)

The optimum shape for a positive lens with one conjugate at infinity is

nearly planoconvex, with the curved side toward the long conjugate. Because

planoconvex lenses are readily available, we limit the discussion to such

lenses.

Smith gives relatively complicated formulas for the third-order aberrations of thin lenses when the stop is in contact with the lens [7]. The

formulas are written in terms of the refractive index of the glass, the conjugates and the shape of the lens. There is no need to reproduce the formulas

here. However, for the special case of a planoconvex lens with one conjugate

at infinity, the formulas reduce to comparatively simple form. These are stated in Table Dl, in which the transverse aberrations are expressed in units

of the Airy-disk radius.

Table Dl

Transverse Aberrations of a Planoconvex Lens^

Aberration Formula

Soherical

Coma

0.120 D

X(f#)3

0.034h

Astigmatism and ^'^^^^

{1+^)

field curvature

X(f#)

0.205

Xf(f#)2

^" "' f(f#)

Value

at 1.06 ]iT!r

1132 D

(f#)3

321h

(f#)3

3223h2

1. In units of 1.22 xf/D.

2. All measurements in centimeters, n = 1.50.

36
The transverse aberrations may be used to estimate the size of the image

of a distant point; Table Dl refers only to a planoconvex lens with the proper

orientation. If the sum of the aberrations in Table Dl is less than 1, then

the image size is about equal to the Airy disk size; the image is said to be

"diffraction limited." If the sum is greater than 1, then the image is about

equal to that many Airy disk radii. (In reality, the semi diameter of the

comatic image in the radial direction is 1.5 times the size given by Table

Dl.) A lens will be acceptable as a collimator provided that the sum of the

aberrations is substantially less than the source size required to yield the

desired beam divergence.

When the source is precisely on the axis of the lens, then only spherical

aberration contributes to the aberration sum; the other aberrations are zero. They are included in the table so that angular tolerance may be calculated as well

.

By way of example, let us consider an F/20 lens, focal length 200 cm and

diameter 10 cm. Let the source be located 2" off axis; then h is 7 cm (see

Fig. Dl). Using the formulas in column 3 of Table Dl, we find that

spherical =1.4

coma =0.3

and

astig. + f.c. = 2.0.

Using 1.5 times coma for the aberration contribution, we estimate the image

semidiameter to be about 4 Airy-disk radii. On the axis, the sphericalaberration contribution is 1.4 Airy disks. This lens is nearly diffraction

limited on the axis, but performs somewhat more poorly 2° off the axis. These

numbers are in good agreement with a raytrace performed on a similar lens [8].

The beam divergence due to diffraction is 1.22 x/D; for this lens, this comes to about 0.01 mrad. At 2° off axis, the beam divergence is less than

0.05 mrad. The lens should be more than adequate to collimate a beam to

divergence of 0.5 mrad or less.

37
Transverse

aberration

Figure Dl. Transverse aberration of a planoconvex lens.

38
Appendix E

Calculation of Power

Here we make a rough estimate of the power expected to be received at 10-

km range by our typical system (Table 4). For the purpose of this calculation, we assume the distant scatterer to be a Lambert diffuser; later, we

shall assume the LEDs to be Lambert sources. The geometry is that of Fig. El. We assume that all the power emitted by

the laser falls onto the diffuser. The fraction of that power that is captured by the receiver may be found from the equation

d2<j) = L dS cos 9 dfi (El)

where L is the apparent radiance of the scatterer and is given by the relati on

,

L = ^Jt^ dS . (E2)

if represents radiant power, dS is the area of the illuminated part of the

scatterer, dfi is the solid angle subtended by the receiver at the scatterer,

and cos 6 is 1 for nearly normal incidence [9].

Because the radiation is uniform over the aperture of the receiver, we may set d^ equal to the (finite) area of the receiver and implicitly integrate

Eq. (El) with respect to fi. The result is that

d(|> =

4.^ d2/4£2 . (E3)

We are more likely to be interested in energy than in power; therefore, we multiply both sides of Eq. (E3) by time and find that

dQ = Q 02/4*2 ,

where Q represents radiant energy. dQ is the total energy that falls onto the

entrance pupil of the receiver, and Q^ is the energy emitted by the laser.

39
Figure El. Geometry for determining energy collected by receiver,

40
Appendix F

Angular Tolerance of Interference Filter

We assume that the interference filters are the metal -dielectric-metal or Fabry-Perot type. The wavelength of maximum transmittance is given by the

equation,

mx = 2d . (Fl)

If the filter is tilted slightly, Eq. (El) becomes

mX' = 2d cos e , (F2)

where X' is the wavelength of the maximum at the angle 9. If x' differs from

X by substantially less than the passband of the filter, then the tilt is

inconsequential

.

We calculate the difference 6x between x' and x by assuming that e is

relatively small and approximating the cosine by the first two terms in its

Maclaurin expansion,

cos e s 1 - e2/2, (F3)

whence,

5X/X = - 62/2 . (F4)

If we demand that 5X be less than the half width ax/2 of the filter, we find

that

e2 < AX/X . (F5)

The passband of the filter of Table 4 is 100 nm and the maximum about

1000 nm. Thus, Eq. {F5) shows that the transmission band will shift aopreciably only if 9 is about 20° or more. Let us therefore say that the angular

tolerance of the filter is about 4°. This is approximately the vertex anale

41
If Qq = 0.1 J, D = 10 cm and Jl = 10 km, then dQ is about 2.5 x 10'^^ J.

Allowing for loss (such as diffuser reflectance's being less than 1), we may

say that the total energy collected by the receiver will be as small as 10" '•^

J or less.

Next, we estimate the energy transmitted from the LED through the lens.

If the LED may be regarded as a Lambert soure, then the power (t)(9) radiated

into a cone with vertex angle 8 is

^{Q) = (f)Q sin ^9

, (E4)

il

where <^q is the power radiated into a hemisphere [9]. Using the relation that

sin e - D/2f' = l/2f# , (E5)

we may write <^{Q) in the form

<l)(e) = (t)Q/(2f#)^ . (E6)

If (t)Q represents the peak power of a pulse whose duration is t, then

Q(e) = (t,^T/(2f#)2 , (E7)

where Q is radiant energy.

If the peak power of the pulses is 4 mW (corresponding to 2- A drive

current in some LEDs) and the duration is 40 ns, then we may expect 10"-^^ J into an F/20 aperture. (If the radiation is filtered, then the energy may be

an order of magnitude less.) In fact, certain LEDs are manufactured with a condensing lens in close contact, so the power at normal incidence may be substantially greater than that predicted for a Lambert source. Actual measurements, including the uniformity of the radiation pattern across the lens aperture, have been left to the experimental sections in the body of the report.

42
of an F/8 cone. Therefore, the filter may be placed into an F/8 cone without

harmful effects. Cones with higher relative aperture than F/8 may be dangerous; in such cases, optics will have to be provided to place the filter in a more-nearly collimated beam.

43
NBS-114A (REV. 0-76)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

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1. PUBLICATION OR REPORT NO. MBS T:I-1031

5, SdcJgti^f* Ag««*sfp8 Ifo*

4. TITLE AND SUBTITLE

The Use of LEDs to Simulate Weak YAG-Laser Beams

5. Publication Date January 1981

^ -- -V- ^-NN - 7. AUTHOR(S)

Matt Young

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DEPARTMENT OF COMMERCE

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Mr. Barry Hardin

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16. ABSTRACT (A 200-word or lesa factual Bummery o{ moat significant information. If document includes a significant bibliography or

literature survey, mention it here.) The purpose of this report is to determine whether and under what conditions a light-emitting diode may be used to simulate a weak YAG-laser beam

that has been scattered by a distant reflecting object. By examining the

differences between laser radiation and LED radiation, we conclude that

there is no theoretical reason that a LED may not be used in place of the

laser beam.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Laser simulator; light-emitting diodes; YA6 laser

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