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An Introduction to Semi-Active Laser (SAL) Designation and Guidance

EE 69212/10/2003

Abstract

Semi-Active Laser (SAL) guidance is used extensively in the modern battlefield on multiple weaponsystems ranging from rockets to missiles to guided bombs. The SAL guidance scheme relies on a laser designator to illuminate a target with reflected light , and the weapon system will contain a seeker, usually aquadrant detector, for homing in on the energy reflected from the target. SAL guidance is a relativelycheap and accurate way of engaging targets , but can be susceptible to degradation in performance due toenvironmental (natural weather) effects and countermeasures. This paper will introduce the equations andconcepts needed to produce SAL synthetic signal data to drive missile simulations. To accomplish thecreation of the synthetic SAL data we shall look at how geometry, beam divergence, target size, and clutter

become factors in the mathematical representation of a pulsed laser illuminated target return signal as seen by the seeker head.Investigating how geometry, beam divergence, target size, and clutter become factors inthe mathematical representation of a pulsed laser illuminated target return signal as seen by the seeker headmust be done in order to create the synthetic SAL data.

Introduction

Invented in 1960, the laser (light amplification by stimulated emission of radiation) has made a valuablecontribution to the modern weapons being used on the battlefield today. The first weapon systemsemploying laser guidance were the Maverick, Copperhead, and Hellfire weapon systems which enteredservice in the late 1970s. These weapon systems employed 1.06 micron semi-active laser homing seekers,which are still being developed for the weapon systems of today. These weapon systems are said to besemi-active because they do not originate the laser energy that they receive and track, in other words , theweapon system does not have a laser source installed but relies on an external laser designator.

A laser beam is a highly focused electromagnetic energy beam which can be thought of a s being coherent.Coherency refers to the fact that all of the energy in the beam is at the same frequency and phase. The useof short wavelengths allow for the creation of a virtually non-spreading laser beam that can be placed onto

a single entity in a target rich environment with little to no energy spill over. Laser designators radiate thenarrow beam of pulsed energy, which allows for the measurement of range using the same techniques as aradar system where the pulse is sent out and the round trip time is divided by two. Many current tacticallasers operate in the near-infrared wavelength spectrum, which is not visible to the human eye. Materialschosen for the production of Continuous Wave (CW) Lasers include Carbon Dioxide (CO 2), Helium-Neon(He-Ne), and Argon (Ar). Materials chosen for the production of Pulsed Lasers include Neodymium withYttrium Aluminum Garnet (YAG) crystals (Nd:YAG), and Gallium Arsenide (GaAs), and Ruby and

Neodymium-Glass (Nd-Glass). Information on the CW and Pulsed Lasers is given in the table below.

CONTINUOUS WAVE (CW) LASERSTYPE WAVELENGTH,

mPOWER, W PULSE

DURATION, nsecPULSE

REPETITION RATECO 2 10.6 1400-1800 N/A N/A

He-Ne 0.633 0.05-0.1 N/A N/AAr 0.514 5 N/A N/A

PULSED LASERSTYPE WAVELENGTH,

mENERGY, J PULSE

DURATION, nsecPULSE

REPETITION RATE Nd:YAG 1.06 0.02-0.04 10-25 100 sec -1

GaAs 0.9 0.0001 100-150 100 sec -1 Ruby 0.694 7-9 3-5 20 min -1


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Nd-glass 0.53 20-30 20 12 hr -1

In the scope of this paper , we will mainly consider the Pulsed Lasers, specifically the Nd:YAG variant willmainly be considered . For a weapon system to achieve semi-active laser guidance , it must use some sort of detection scheme to resolve the energy from the laser designator. Within the scope of this paper , we will

consider a four quadrant detector scheme to resolve the reflected energy, whereas a defocused image (spot)will be projected onto the four quadrants to allow the weapon to calculate pitch and yaw needed tocommand the weapon to guide itself to the source of the energy (the reflection of the energy off of thetarget surface) will be considered .

Theory

The laser beam that a laser designator emits is a narrow beam of pulses that has characteristics of being asingle color (single wavelength) and divergent. Laser designation suffers from qualities such as beamdivergence, spot jitter, attenuation, backscatter, overspill, and underspill. The laser spot size at the target isa function of the range from the designator to the target to the beam divergence. Beam divergence isdefined by the fact that as the range from laser designator to the target being designated increases, then thelaser spot diameter at the target increases. The quantity of beam divergence will differ between types of designators because of differences in the optics of each designator. Spot jitter is the product of motion of the laser designator and atmospheric disturbances producing a random movement of the laser spot about theintended aim point. A certain portion of the laser beam energy that is scattered by obscurants andatmosphere resulting in reduced laser energy as seen by the seeker ;, this condition is known as attenuation.Laser energy can be scattered back in the direction of the seeker off of atmospheric particles or obscurantssuch as dust or smoke in the laser path , ; this condition is known as backscatter. Backscatter energycompetes with the reflected energy from the true target, and the seeker may lock onto the energy fromobscurant rather than the true target. Overspill and underspill is caused by either placing the laser spot toohigh or too low on the target so that beam divergence and spot jitter cause the spot or a portion of the spotto spill over onto an object or the terrain behind or in front of the true target. Overspill and underspill cancause intermittent background and foreground false targets. [1]

Beam Divergence

For a coherent monochromatic light source, such as a laser, beam divergence is primarily affected by the beam exit diameter and wavelength. The equation for a plane wave source is [2]:

beam FA d

4=

where:

FA is the Full-Angle Divergence in radians. is the wavelength in meters.

beamd is the initial beam diameter in meters.

Spot Radius

In the late 1970 s, an empirical algorithm was developed to compute laser beam spread as a function of range, atmospheric turbulence, and other laser characteristics. The equation cited for beam radius, r final , of alaser at range to the target, Rtgt , is as follows [3]:

5/63/525/22222222 ))/)(((2.6)//())/(1( ds R s sC k Rr k R f Rr r tgt ntgt beamtgt tgt beam final ++= where:

beamr is the initial radius from the output of the designator ( 2/beamd ). f is the optical system focal length.k is the wave number (2 /).

Table 1. Specific Laser Values.


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is the wavelength.C n is the refractive index structure (atmospheric turbulence parameters) constant.

The first term within this equation accounts for the geometrical optics associated with the laser, an initiallydiverging beam is correspondent to a negative focal length. This may be realized in figure below where r 1 is the radius due to the half-angle divergence, , where = 2/ FA .

From the figure above:22

1 )( tgt beam Rr r += This corresponds to the first term in the equation for the beam radius if f=-r beam / .The second term in the beam radius equation is due to diffraction.

222 )/( beamtgt kr Rr =

The third term in the beam radius equation is due to the turbulence, if the turbulence is constant over thelaser path, then:

5/165/125/223 9.1 tgt n RC k r =

If the laser path is divided into n equal segments, and C n2 is measured for each segment, the third term in

the equation becomes:

+++=tgt

tgt

tgt

tgt

tgt R

n Rnn

n R

n Rn

n R

n ds snC ds sC ds sC k r /)1(

5/63/52/2

/

3/52/

0

3/525/223 ))(...)2()1((2.6

which simplifies to:5/622

22

15/165/165/22

3 ))(...)2()1(()/1(9.1 nC K C K C K Rnk r nnnntgt +++= where:

K 1= 1 , K 2= 28/3-1, K 3= 3

8/3-28/3, , K n= n8/3-(n-1) 8/3

It should be noted that the integration is from the target to the laser, which causes the turbulence effects to be biased more toward the laser; in other words, strong turbulence near the laser results in a larger beam atthe target than strong turbulence near the target.

The final laser beam radius at the target range can now be expressed as:2

32

22

1 r r r r final ++=

Laser Designator Range Equations

In most of the calculations that we will be interested inused for laser designation , we it can be assume d thatwe it will be in the near-field or Fresnel region where the laser cross section of the target must be carefullyconsidered. The equation to be in the far field, i.e. where the radiation is approximately planar [1], is:

Figure 1. Beam Spread due to Divergence.


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22 o D R >

where:2o D is the diameter of the optics (aperture) squared

As an example, for a wavelength of 1.06m we have the following:

Aperture (in) Onset of Far Field (m)1 1217.282 4869.133 10955.554 19476.535 30432.086 43822.197 59646.878 77906.11

The laser cross section of a target for applications in the near-field is defined as [1]:

= dA 4

where: is the scattering solid angle of a target in steradians. is the target reflectivity.dA is the illuminated area of target.

The value of is dependent upon the type of surface illuminated. For laser scattering with diffuse targets ,

we it can be assume d that it is a Lambertian target scattering model, and therefore = . Lambertiantargets are typically assumed , when scattering peaks in the specular direction falls off as the scatteringdirection moves away from specular [1].

We shall consider three Three cases for calculating the power received at the seeker dome that istransmitted from the designator are considered . The three cases shall consist of a resolved target (where thetarget is larger than the beam), an unresolved target (where the beam is larger than the target), and a clutter target (where the beam is illuminating ground clutter).

The resolved target case is shown in the figure below.

Table 2. Far Field Values for 1.06m Laser.


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The equations governing the above scenario for a resolved target are as follows [1], [4]:

The above equation for the received power for the resolved target case simplifies to:

2

cos

S

asad S T R R

T T A P P

=

where:

T P is the laser energy in one pulse transmitted from the designator.

S A is the area of the seeker aperture

ad T is the atmospheric transmission in the path from the laser designator to the target, which is a functionof laser wavelength, visibility, designator range and altitude.

asT is the atmospheric transmission in the path from the target to the seeker, this parameter is also afunction of laser wavelength, visibility, seeker range (R s) and the seeker altitude.

cos is the cosine of the angle between the laser designator path and the seeker path. The inclusion of cos in the equation results from the assumption that the target surface is a Lambertian reflector (when

= 0, reflectivity is maximum, and when approaches 90 the reflectivity approaches zero).

The unresolved target case is shown in the figure below.

Figure 2. Resolved Target Scenario [4].


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The equations governing the above scenario for an unresolved target are as follows [1], [4]:

The above equation for the received power for the unresolved target case simplifies to:

2222

cos4

FAS D

asad S T T R R R

T T A P P

=

The clutter target case is shown in the figure below.

The equations governing the above scenario for a clutter target are as follows [1], [4]:

Figure 3. Unresolved Target Scenario [4].

Figure 4. Clutter Target Scenario [4].


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The above equation for the received power for the clutter target case simplifies to:

sincos

2S

asad S T R R

T T A P P =

Noise equivalent power (NEP) can be defined as the power or intensity of radiation that must be incidenton a detector in order to produce a signal equal to the intrinsic noise of the detector. The equation for the

NEP can be given as follows [1]:

Watts, *d

D

D

F A NEP

=

where:

D A is the area of the detector in cm 2. F is the electrical noise bandwidth.

*d D is the specific detector detectivity.

The signal-to-noise ratio, often abbreviated SNR or S/N , is a term for the ratio between the maximum possible signal and the background noise, and can be useful for the tracking of targets. The received SNR at the semi-active laser seeker for a resolved Lambertian target is given as follows [1]:

F A R

DT T A P NEP

P SNR

DS

d asad S T R

==

2

*cos

Because many signals have a very wide dynamic range, SNR is usually expressed in terms of thelogarithmic decibel scale. The SNR in decibels is 10 times the logarithm of the power ratio and can becalculated as follows:

)(log10 10 SNRSNRdB = Another useful calculation to determine if a seeker can track a specific target that is being illuminated is thesignal-to-threshold ratio (S/T). S/T defines the ratio of the laser signal strength at the seeker to the seeker threshold. If the S/T value is one or greater then the seeker can track the target but if the S/T is less thanone the target cannot be tracked. S/T is defined as follows [3]:

TH S

asad d

E R P T T E

T S 2cos)(

/

=

where:

d E is the laser pulse energy in Joules from the designator.

P is the percentage of the laser beam that falls on the true target.

TH E is the seeker threshold in Joules/cm2 which can be a constant value or be designed to be a function of

the NEP.

Quadrant Detector Guidance Scheme


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Laser energy reflected from the target enters the front, or dome optics, of the weapon system. The domeoptics includes a band-pass filter to block energy outside the 1.06 m laser wavelength. The high contrastimage of the laser spot is defocused on to a photodetector assembly, mounted directly behind the dome.The photodetector is usually a quad cell detector, which is a photodiode whose active area is partitionedinto four discrete quadrants. This scheme is shown in the figure below.

The defocused spot is projected onto the four quadrants to allow currents to flow. These currents can betaken as a measure of how much energy in the defocused spot lies on each specific detector. Next, azimuthand elevation corrections can be calculated from this data (see equations for EL and AZ from figureabove), and the weapon system can use this information to steer itself onto a collision course with thesource of the reflected energy.

Conclusion

The information and equations presented within this paper represent a basis for the formulation of simplistic synthetic SAL signal generation, as well as the needed guidance to control a SAL guided weaponflight path to a reflected energy return. The equations as presented allow for the use of a rectangular flat

plate simple target, but could be easily modified to use high-fidelity facetized target geometry with multiple parts and different values of reflectance. Some of the current downfalls of simulating laser energy returnsfrom high-fidelity geometry have to do with the time that it takes to simulate each specific facet of themodels, but with new techniques such as hardware accelerated graphics and OpenGL the time taken to

process these simulations should dramatically decrease.

Do not use any personal 1 st or 2 nd voice pronouns (I, me, we, us, you) in a technical paper!!!!! Itdetracts from the technicality and makes it sound like a story.

References

[1] Class Notes: Tri-Mode Seeker Technologies - UAH Professional Development - Berinato 2003[2] Photonics Rules of Thumb: Optics, Electro-Optics, Fiber Optics, and Lasers - John Lester Miller [3] Generation of Laser Energy Returns to Drive Laser Designated Weapon Systems - August 1980

Figure 5. Quadrant Detector Scheme [5].


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[4] Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Klein[5] ERIM The Infrared Handbook - Wolfe/Zissis 1989/1993 [6] Introduction to Sensor Systems - Hovanessian[7] RCA Electro-Optics Handbook

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