Post Reply 
(HP-67/97) RADAR - Speckle Target Calculations
01-26-2019, 07:29 PM
Post: #1
(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


BEST!
SlideRule
Find all posts by this user
Quote this message in a reply
01-27-2019, 08:29 AM (This post was last modified: 01-28-2019 07:23 PM by StephenG1CMZ.)
Post: #2
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)
https://my.numworks.com/python/steveg1cmz
Visit this user's website Find all posts by this user
Quote this message in a reply
01-27-2019, 11:59 AM
Post: #3
RE: (HP-67/97) RADAR - Speckle Target Calculations
PM sent
Find all posts by this user
Quote this message in a reply
01-27-2019, 01:18 PM
Post: #4
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)

BEST!
SlideRule
Find all posts by this user
Quote this message in a reply
01-27-2019, 06:15 PM
Post: #5
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
Find all posts by this user
Quote this message in a reply
Post Reply 




User(s) browsing this thread: 2 Guest(s)