(HP-67/97) RADAR - Speckle Target Calculations
01-26-2019, 07:29 PM
Post: #1
 SlideRule Senior Member Posts: 947 Joined: Dec 2013
(HP-67/97) RADAR - Speckle Target Calculations
An extract from Turbulence Effects …, MIT, TST-33, 1979 JUL (98 pages).

… programs for performing speckle target calculations on … HP-67, HP-97 programmable calculators … included in an Appendix …

APPENDIX. PROGRAMMABLE HAND CALCULATOR PROGRAMS pg-87

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SlideRule
01-27-2019, 08:29 AM (This post was last modified: 01-28-2019 07:23 PM by StephenG1CMZ.)
Post: #2
 StephenG1CMZ Senior Member Posts: 794 Joined: May 2015
RE: (HP-67/97) RADAR - Speckle Target Calculations
Archive.org seems to be unreachable from the uk... Using Vodafone.
Update: Rather than simply failing, Vodafone now reports an age-related block to archive.org (unless a credit card is provided).

Stephen Lewkowicz (G1CMZ)
01-27-2019, 11:59 AM
Post: #3
 SlideRule Senior Member Posts: 947 Joined: Dec 2013
RE: (HP-67/97) RADAR - Speckle Target Calculations
PM sent
01-27-2019, 01:18 PM
Post: #4
 SlideRule Senior Member Posts: 947 Joined: Dec 2013
RE: (HP-67/97) RADAR - Speckle Target Calculations
(01-27-2019 08:29 AM)StephenG1CMZ Wrote:  Archive.org seems to be unreachable from the uk... Using Android and Vodafone.

Also available at Turbulence Effects … (dtic.mil)

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SlideRule
01-27-2019, 06:15 PM
Post: #5
 Thomas Klemm Senior Member Posts: 1,448 Joined: Dec 2013
RE: (HP-67/97) RADAR - Speckle Target Calculations
From page 13.

Eq. (11) becomes

$$P_D=\frac{1}{\sqrt{\pi}} \int_{-\infty}^{\infty} \: d\tau \: e^{-\tau^2} \: P_F \: ^{\frac{1}{1 \, + \, CNR_s \, e^{2\sigma(\tau\sqrt{2}-\sigma)}}}$$

$$(21)$$

Eq. (21) has a form suitable for Gaussian-Hermite quadrature. A 16-point quadrature provided sufficient accuracy for $$\sigma^2 \leq 0.2$$. For larger $$\sigma^2$$ values the number of quadrature points was increased to 32.

From APPENDIX, page 87.

PROGRAMMABLE HAND CALCULATOR PROGRAMS

Evaluation of the speckle target detection probability Eq. (21 ) is straightforward and yields excellent accuracy for quadratures with a relatively small number of points. This, coupled with the fact that most objects exhibit a significant diffuse reflection component at optical and infrared wavelengths, has prompted us to develop a program suitable for evaluation on a programmable hand calculator. In Table 21 we detail a program usable with either a Hewlett-Packard HP-67 or HP-97 calculator. This program calculates $$P_D(CUR_s;P_F,\sigma^2)$$ for $$P_F$$ stored in register A, $$\sigma^2$$ stored in register B, and $$CNR_s$$ entered as $$x$$ using an 18-point Gaussian-Hermite quadrature. The quadrature points and weighing coefficients are entered via a data card. Computation time of this program is roughly 60 seconds and the relative accuracy in $$P_D$$ is better than about 0.3%, for $$\sigma^2 = 2.0$$ and improves rapidly as $$\sigma^2$$ decreases.

The preceding programs were also modified for use with a Hewlett-Packard HP-29C calculator. The modified programs are detailed in Table 22. Because of the larger number of storage registers available, a 24—point Gaussian-Hermite quadrature was used. Computation time of this program is roughly 75 seconds and the relative accuracy in $$P_D$$ is approximately 0.03% for $$\sigma^2 = 2.0$$ and improves rapidly as $$\sigma^2$$ decreases.

Nodes and Weights

These tables were calculated with the Nodes and Weights of Gauss-Hermite Calculator.

n = 18
Code:
1    0.2582677505190967592581  0.4834956947254555528764
2    0.7766829192674116613167  0.284807285669979578596
3    1.300920858389617365666   0.0973017476413154293309
4    1.835531604261628892254   0.01864004238754465192193
5    2.386299089166686000265   0.00188852263026841789438
6    2.961377505531606844779   9.18112686792940352915E-5
7    3.573769068486266079501   1.810654481093430409597E-6
8    4.248117873568126463023   1.046720579579208244436E-8
9    5.048364008874466768372   7.8281997721158910293E-12

n = 24
Code:
1    0.2244145474725155851511  0.4269311638686992496532
2    0.6741711070372122360003  0.2861795353464430179019
3    1.126760817611245072133   0.1277396217845591606473
4    1.584250010961694148506   0.03744547050323074601333
5    2.04900357366169891179    0.00704835581007267097
6    2.523881017011426974199   8.23692482688417457918E-4
7    3.012546137565564825655   5.68869163640437976904E-5
8    3.52000681303452471129    2.15824570490233363224E-6
9    4.053664402448149503948   4.01897117494142968454E-8
10    4.625662756423787265049   3.04625426998756390389E-10
11    5.259382927668044367431   6.58462024307817006456E-13
12    6.01592556142573971735    1.66436849648910887377E-16

It's interesting to note that these values were arranged differently in the registers of the HP-67 and the HP-29.
In case of the HP-67 the primary and secondary banks were swapped using the P<>S command.
But since these registers were only addressed indirectly the same approach as for the HP-29 could have been used.

Efficiency

Both program could be improved, though I consider the 2nd one for the HP-29 slightly better.
At least they knew that they could swap $$x$$ and $$y$$:

HP-67
Code:
050 STO D
051 RCL A
052 RCL D
053 h yˣ

HP-29
Code:
047 RCL 3
048 x↔y
049 f yˣ

It appears they were not aware of the LAST X command.
Both programs use:
Code:
RCL B
√x
-
RCL B
√x
×

The register B contains the parameter $$\sigma^2$$ which is constant during the calculation.
They could have stored $$\sigma$$ instead of calculating the square root twice in the loop again and again.

Cheers
Thomas
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