NASA/TM–2014-217516

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Energy Replicated Optics To Explore The Sun Mission 
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May 2014

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Energy Replicated Optics To Explore The Sun Mission 
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 %DFNJURXQG

2.1 Introduction

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3<$6LQWKDWPLVVLRQ7KHUHOHYDQWGHWDLOVRIWKH3<$6RSWLFDOPHFKDQLFDODQG

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MXVWLILHGEDVHGRQWKH3<$6KDUGZDUHDQGDUHLPSRUWDQWIRUNHHSLQJWKH3<$6

SURFHVVLQJSUREOHPWUDFWDEOH

2.2 PYAS System Requirements

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UHTXLUHPHQWV7KH3<$6ZDVH[SHFWHGWRSURYLGHSLWFKDQG\DZRIIVHWVIURPDWDUJHW

DQ\ZKHUHRQWKHVXQZLWKDQDFFXUDF\RIEHWWHUWKDQDUFVHFRQGVWRWKHJRQGRODFRQWURO

V\VWHP&7/DQGWRGRVRZLWKDFDGHQFHRI+](DFKIUDPHDOVRQHHGHGWREHVDYHG

IRUSRVWSURFHVVLQJRQWKHJURXQG7KHVHVROXWLRQVKDGWREHJHQHUDWHGDQ\WLPHWKHVXQ

ZDVZLWKLQWKHILHOGRIYLHZ)29RIWKH3<$67KH+(52SD\ORDGZDVFDSDEOHRI

SRLQWLQJZLWKDQDFFXUDF\RILQSLWFKDQG\DZRQFRDUVHVHQVLQJDORQHDWZKLFKSRLQW

LWGHSHQGHGRQILQHVHQVLQJWRVWDELOL]HRQDWDUJHW)RUVRODUSRLQWLQJWKHWDUJHWFRXOGOLH

DQ\ZKHUHRQWKHVXQ%HFDXVHWKHVXQLVURXJKO\DFURVVHQVXULQJWKHVXQZDVDOZD\V

IXOO\RQWKHVFUHHQDIWHUFRDUVHSRLQWLQJUHJDUGOHVVRIZKHUHWKHWDUJHWZDVSODFHGRQWKH

VXQZRXOGUHTXLUHDWOHDVWD)297KH3<$6ZDVRQO\DEOHWRDFKLHYHD)29VR


LWZDVGHFLGHGWKDWLWZRXOGRQO\EHUHTXLUHGWRSURYLGHDFRDUVHVROXWLRQIRUDSDUWLDOO\

YLVLEOHVXQ%HFDXVHRIWKHQDUURZ)29RIWKH[UD\WHOHVFRSHDFFXUDF\DWWKHHGJHVRI

WKH)29ZDVOHVVLPSRUWDQW'HJUDGHGVROXWLRQVZHUHSHUPLVVLEOHWKHUHDVWKH\RQO\KDG

WREHDFFXUDWHHQRXJKWRWHOOWKH&7/URXJKO\ZKHUHWRVOHZWREULQJWKHVXQIXOO\RQWR

WKHVFUHHQ$VXPPDU\RIWKHUHOHYDQWUHTXLUHPHQWVRQWKH6$6DUHVKRZQLQ7DEOH

7KHHQWLUHV\VWHPLVDFORVHO\FRXSOHGSDLURIERWKKDUGZDUHDQGVRIWZDUHEXWWKHIRFXV

KHUHZLOOEHRQVRIWZDUH6SHFLILFDOO\WKLVZLOOEHDGHWDLOHGGHVFULSWLRQRIWKHDOJRULWKP

XVHGIRUFRQYHUWLQJUDZ3<$6LPDJHVLQWRSLWFKDQG\DZRIIVHWV

Requirement Minimum Target

&DGHQFHVWRUDJH +] +]

&DGHQFHSURFHVVLQJ +] +]

$FFXUDF\IOLJKW DUFVHFRQGV DUFVHFRQGV

$FFXUDF\SRVWIOLJKW DUFVHFRQGV DUFVHFRQGV

)29  ILQH

!FRDUVH

Table 1: List of relevant requirements for the HEROES PYAS

2.3 PYAS System Overview

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ORFDWLQJWKHSURMHFWHGLPDJHRIWKHVXQUHODWLYHWRWKHILGXFLDOV

Figure 1 Diagram of the PYAS optics for a single PYAS system

Fiducial 

Plate

Camera

IR Filter

Solar Lens

Band-pass 

filter

Baffles


Figure 2 Fiducial Pattern. Diagram shows outline of the fiducial plate in red, with the pattern itself 

marked in black.

Figure 3 Example of a typical PYAS frame


2.4 PYAS Images

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Figure 4 Fiducial Spacing. Fiducial spacing along a row is shown here. Subsequent entries along a 

row are spaced vertically by a fixed distance b. Horizontal spacing starts at distance a near the center 

of the screen and increases by c for each subsequent column

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DOXPLQXPSODWH7KHSDWWHUQLVODLGRXWLQVXFKDZD\WKDWPDUNHUVFDQEHLGHQWLILHG

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Figure 5 Examples of disturbances in PYAS image. (Left) Bright spot at the edge of the fiducial plate, 

probably due to light leaking through the baffle. (Right) Bright spots which are likely scratches on 

the fiducial plate.

2.5 PYAS Imager

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WRPHHWWKH3<$6FDGHQFHUHTXLUHPHQWVHYHQZKHQUHWXUQLQJWKHIXOOLPDJHUDWKHUWKDQD

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FRPELQHGZLWK)29JDYHHDFKLPDJHSL[HODQDSSUR[LPDWHZLGWKRI

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DVL]HDEOHPDUJLQDJDLQVWWKHUHTXLUHPHQW

Camera Parameters

&DPHUD ,PSHU[,*9%

/HQV 09//PPOHQV

,PDJHVL]H [SL[HOV

%LW'HSWK&RORU ELWPRQRFKURPH

XVHG

0D[)UDPHUDWH )36

Table 2: PYAS Camera parameters

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DQG5$6LPDJHDQGDOOFRPPDQGDQGWHOHPHWU\IXQFWLRQV7KHFRPSXWHUVWDFNZDV

DVVHPEOHGIURPRIIWKHVKHOIFRPSRQHQWVFRQIRUPLQJWRWKH3&VWDQGDUG7KHUH

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GLUHFWO\UHOHYDQWWRWKH3<$6DOJRULWKP7KHVSHFVIRUERWKDUHOLVWHGEHORZ


SBC

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3URFHVVRU ,QWHO$WRP1

6LQJOHFRUH

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5DP *%''5

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Storage

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Table 3 Summary of relevant SAS computer specs.

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PHDQWWKDWWKHSURFHVVLQJDOJRULWKPZDVWLPHVKDULQJZLWKFRPPDQGWHOHPHWU\DQGGDWD

VWRUDJHIXQFWLRQV7KHFORFNUDWHZDVDOVRORZUHODWLYHWRRWKHUPRGHUQSURFHVVRUVZKLFK

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FKRVHQWREH66'VL]HGWREHDEOHWRVWRUH3<$6GDWDXQFRPSUHVVHGIRUKRXUVRI

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IXOOXQFRPSUHVVHG3<$6DQG5$6IUDPHVDW+]

2.6 PYAS Assumptions 

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SUREOHPPLJKWKDYHWRKDQGOH7KHUHDUHVFHQDULRVQRWGHVFULEHGDERYHKRZHYHUZKLFK

FRXOGVHYHUHO\DOWHUWKHVFHQHREVHUYHGE\WKH3<$6FDPHUD$FFRXQWLQJIRUHYHU\

SRVVLEOHDQRPDO\ZRXOGYHU\TXLFNO\SXVKWKHDOJRULWKP
VFRPSOH[LW\WRDSRLQWZKHUHLW

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PDGHDERXWKRZ3<$6IUDPHVPLJKWYDU\GXULQJIOLJKWZLWKWKHJRDORINHHSLQJWKH


3<$6SUREOHPWUDFWDEOH7KHVHDVVXPSWLRQVDUHOLVWHGLQ7DEOHDQGDGLVFXVVLRQRIWKH

LPSDFWDQGYHULILFDWLRQRIHDFKZLOOEHJLYHQEHORZ

Assumption

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 2SWLFVDQGFDPHUDDUHDSSUR[LPDWHO\SDUDOOHOWRWKHILGXFLDOSODWH

D 6RODULPDJHLVFLUFXODUUDWKHUWKDQHOOLSWLFDO

E 3URMHFWLYHDIIHFWVIURPWKHFDPHUDRULHQWDWLRQFDQEHDSSUR[LPDWHGZLWKDVLPLODULW\WUDQVIRUP

F &ORFNLQJRIILGXFLDOSODWHUHODWLYHWRWKHFDPHUDLVQHJOLJLEOH

G &KDQJHLQGLVWDQFHDQGFORFNLQJEHWZHHQILGXFLDOSODWHDQGFDPHUDZLOOEHVPDOO

 7KHSURMHFWHGVRODULPDJHZLOOQRWEHXQGHURURYHUH[SRVHG

Table 4 PYAS Flight Assumptions

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3.1 Introduction

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3.2 Sun Sensors

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Table 5 Summary of sun sensors FOV, accuracy, and cadence

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Figure 7 Illustration of Template matching. Top left is an example image with three circles. Top 

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correlation from a simple template, bottom center is the correlation from the optimized filter, and 

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screen.

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3.4 Summary

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4.1 Algorithm Structure

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Stage Input (space) Output (space)

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Table 7 PYAS Algorithm Stages

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4.2 Locating the Sun

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Figure 9 Effective chord placement in RHESSI (left) versus HEROES (right)


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Table 8 Ideal criteria for a valid chord through the sun

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1. Input: past_ROI_location, current_frame, K, N 

2. robust_max = 99th percentile of pixel values of current_frame.

3. Robust_min = 1st percentile of pixel values of current_frame

4. threshold = K% of robust_max

5. if past_frame produced valid solution

chords = N rows and N columns evenly across past_ROI_location in current_frame

else

chords = N rows and N columns spaced evenly across entire current_frame

6. for each chord in chords

a. for each pixel in chord

if current_pixel > threshold AND past_pixel < threshold

edges <- current_pixel_index

 if current_pixel < threshold AND past_pixel > threshold

 edges <- -1*past_pixel_index

b. for each edge in edges 

 if |current_edge| – |past_edge| < fiducial_length

 remove current_edge and past_edge from edges

c. if number of elements in edges is 2 AND first_edge > 0 AND last_edge < 0

 for each edge

 nbhd = pixels before and after pixel at edge

 line = fit line to neighborhood

limb = index where line(index) equals threshold

 if chord was row

row_limbs <- limb

else chord was column


 col_limbs <- limb

7. sun_center = [(average of col_limbs) (average of row_limbs)] 

8. sun_error = [(std dev of col_limbs) (std dev of row_limbs)]

9. ROI = 255 pixel square centered around sun_center

10. Output: sun_center, sun_error, ROI, robust_max, robust_min

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SDWFKRIIUDPHLOOXPLQDWHGE\WKHVXQ,WDOVRUHWXUQVWKHVWDQGWKSHUFHQWLOHFXWRIIV

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Error Case Explanation

robust_max – robust_min < range_threshold '\QDPLFUDQJHWRRORZ

size( col_limbs ) < 2 

OR

size( row_limbs ) < 2

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sun_error < error_limit &KRUGPLGSRLQWVDUHWRRVSUHDGRXW

Table 9 Error checks after the sun-finding stage of the PYAS algorithm

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4.3 Locating Fiducials

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1. Input: ROI, robust_max, K1, K2, NBHD_SIZE

2. for each pixel in ROI

if pixel_value > robust_max

pixel_value = robust_max

3. mean = mean of ROI pixel values

4. std = standard deviation of pixel values

5. threshold = mean + K1*std

6. load stored fiducial_template

7. convolve ROI with fiducial_template -> response

8. for each response_pixel in response

if response_pixel_value > threshold

if response_pixel_value is a local max

for each fiducial_pixel in fiducials

 if fiducial_pixel - response_pixel < fiducial_length

 if response_pixel_value > fiducial_value

 fiducial_pixel = fiducial_value

 else

 skip to next response_pixel

 else

 add response_pixel to fiducials

9. if number of fiducials > 12

sort fiducials by value

keep 12 with highest response value

10. threshold = mean + K2*std

11. for each fiducial_pixel in fiducials

nbhd = subimage of response with size NBHD_SIZE centered on fiducial_pixel

refine = centroid of pixel in nbhd with value > threshold

fiducial_pixel = fiducial_pixel + refine

12. Output: fiducials

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4.4 Identifying Fiducials 

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1. Input: fiducials, tol, fixed_spacing, id_spacings

2. all_pairs = list of all pairs of fiducials 

3. for each pair in all_pairs

if (row_spacing(pair) – fixed_spacing) < tol

 add pair to col_pairs

if (col_spacing(pair) – fixed_spacing) < tol

 add pair to row_pairs

4. for each pair in row_pairs

for each row_id_spacing in id_spacings

if (row_spacing(pair) – row_id_spacing) < tol

 for each member in pair

 add row_id to member_row_ids

5. for each fiducial

if mode(member_row_ids) is unique

fiducial_id_row = mode(member_row_ids)

else

fiducial_id_row = unknown

6. Repeat 4 and 5 for columns

7. for each pair in row_pairs

for each member in pair

if member_id_col is unknown

 if other_member_id_col is known

 member_col_ids <- other_member_id_col

8. for each fiducial

if fiducial_id_col is unknown

if mode(fiducial_col_ids) is unique

 fiducial_id_col = mode(fiducial_col_ids)

9. Repeat 7,8 for columns

10. for each fiducial in fiducials

if fiducial_id_row is unknown or fiducial_id_col is unknown

remove fiducial from fiducials

11. Output: fiducials, fiducial_ids 

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4.5 Mapping to Screen

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1. Inputs: fiducials, fiducial_ids, screen_locations, sun_center

2. screen_fiducials = screen_locations(fiducial_ids)

3. for each axis in [row, column]

mappings_axis = linear_fit(fiducials, screen_fiducials)

screen_center_axis = mapping_axis(center_axis) 

4. Output: mappings, screen_center

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4.6 Summary

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5.1 Introduction

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5.2 Synthetic Data

 6XQ)LQGLQJ

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VFDOHRIDUFVHFRQGVSHUSL[HOWKHQGRZQVDPSOLQJWKHLPDJHE\DIDFWRUWR

DSSUR[LPDWHWKHLGHDO3<$6LPDJHVFDOH$IWHUDVLPSOH*DXVVLDQEOXUDQGWKHDGGLWLRQ

RIVRPHZKLWHQRLVHWKHVHLPDJHVDUHDIDLUDSSUR[LPDWLRQRIDFWXDO3<$6LPDJHVZLWK

JURXQGWUXWKJLYHQE\WKHVFDOHGFRRUGLQDWHVRIWKHVXQFHQWHULQWKHRULJLQDOLPDJH7KH

3<$6VXQWUDFNLQJDOJRULWKPZDVWHVWHGDJDLQVWWKHVHLPDJHVDQGSHUIRUPDQFHZDV

PHDVXUHGDJDLQVWQXPEHURIFKRUGVDQGOHYHORIZKLWHQRLVH1RLVHOHYHOYDULHGEXWWKH

SDUDPHWHUVEHORZGHVFULEHWKHRWKHUSDUDPHWHUVRIWKHVHWRIWHVWLPDJHV

Parameter Value

5DQJHRIFHQWHUV WRDUFVHFRQGVLQHDFKD[LV

6XQGLDPHWHU SL[HOV

2YHUVDPSOLQJIDFWRU

DUFVHFRQGWRSL[HOV



Table 10 Parameters for synthetic sun test images

Figure 10 Cropped PYAS image from sun test data (left). Synthetic sun image used in testing (right)


7KLVVWDJHRIWKH3<$6DOJRULWKPKDVWZRSDUDPHWHUVZKLFKFDQEHWXQHGWRDIIHFW

UHVSRQVHWKUHVKROGOHYHO.DQGQXPEHURIFKRUGV1,QDOOWHVWVWKHWKUHVKROG.ZDVVHW

WRRIPD[EULJKWQHVV,QWKLVWHVW1ZDVYDULHGWRVHHWKHHIIHFWRIWKHQXPEHURI

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WHVWZDVKHOGIL[HGDWDOHYHOVLPLODUWRWKDWRIJURXQGWHVWGDWD7KHSDUDPHWHUVIRUWKLV

WHVWDUHWDEXODWHGLQWKHWDEOHEHORZ

Parameter Value

1RLVH6WG'HY FRXQWV

7KUHVKROG FRXQWV

1XPEHURI&KRUGV1 WRSHUD[LV

Table 11 Parameters for test of performance vs number of chords

 7KHUHVXOWVDUHVKRZQEHORZ7KHFHQWHUGHWHUPLQHGE\WKLVDOJRULWKPZDVFRPSDUHG

WRWKHLGHDOFHQWHUDQGWKHPDJQLWXGHRIWKLVHUURUZDVXVHGWRPHDVXUHSHUIRUPDQFH7KH

SORWEHORZVKRZVWKHVLJPDHUURULQDUFVHFRQGVRYHUDOOSRVLWLRQVIRUDJLYHQQXPEHURI

FKRUGV7KHUH¶VFOHDUO\DVKDUSLPSURYHPHQWLQSHUIRUPDQFHLQLWLDOO\ZKLFKVWDUWVWR

IODWWHQRXWDIWHUFKRUGVSHUD[LV%DVHGRQWKLVWHVWWKHQXPEHURIFKRUGVWREHXVHGLQ

IOLJKWZDVVHWDW


Figure 11 Performance vs. number of chords. Error shown is 3sigma of error values for each 

parameter value.

 7KHQH[WWHVWXVHGDIL[HGQXPEHURIFKRUGVDQGYDULHGWKHQRLVHOHYHOWRVHHKRZ

VHQVLWLYHWKLVPHWKRGLVWRLQFUHDVHGQRLVH$UDQJHRIYDOXHVZHUHXVHGIRUVLJPDIURP

QRLVHIUHHWRDQRUGHURIPDJQLWXGHZRUVHWKDQWKHH[SHFWHGQRLVHOHYHO$JDLQ

SDUDPHWHUVIRUWKLVWHVWDUHWDEXODWHGLQWKHWDEOHEHORZ

Parameter Value

1RLVHVLJPD WRFRXQWV

7KUHVKROG FRXQWV

1XPEHURI&KRUGV1 SHUD[LV

Table 12 Parameters for test of chord finding vs noise

$VEHIRUHSHUIRUPDQFHFDQEHPHDVXUHGLQWHUPVRIVLJPDHUURUYHUVXVQRLVHOHYHO

$OVRRILQWHUHVWKRZHYHULVQXPEHURIFKRUGVGURSSHG7KHOLNHOLKRRGRIDFKRUGIDLOLQJ

WRPHHWWKHFULWHULDOLVWHGDERYHIRUDYDOLGFKRUGLQFUHDVHVZLWKQRLVHOHYHO$WDFHUWDLQ

SRLQWQRYDOLGFKRUGVZLOOEHIRXQGLQWKHLPDJH$OWKRXJKLWLVXQOLNHO\WKDWVXFKDKLJK

OHYHORIQRLVHZRXOGEHHQFRXQWHUHGRQIOLJKWLWZDVRILQWHUHVWLQGHYHORSPHQWWRVHH


KRZUREXVWWKLVPHWKRGLVWRKLJKOHYHOVRIQRLVH3ORWVRIERWKHUURUYVQRLVHDQG

GURSSHGFKRUGVYVQRLVHDUHVKRZQEHORZ

Figure 12 Plots of error and percentage of dropped chords vs. noise level. Noise level is measured in 

bits in the intensity, and chords are dropped when they fail to meet the criteria outlined in Chapter 4

)URPWKHSORWRIHUURUZHVHHWKDWEH\RQGQRLVHOHYHOVRIFRXQWVRUVRWKHVXQ

WUDFNLQJDOJRULWKPIDLOVWRPHHWUHTXLUHPHQWVDWDOO$WWKHHYHQKLJKHUOHYHORIFRXQWV

ZHVHHWKDWWKHQXPEHURIYDOLGFKRUGVSOXPPHWVFRUUHVSRQGLQJWRDVSLNHLQHUURU7KH

KRSHZDVWKDWQRLVHOHYHOVLQIOLJKWGDWDZRXOGEHVLJQLILFDQWO\OHVVWKDQWKLV

 7KHODVWWHVWRIWKLVDOJRULWKPZDVGHVLJQHGWRVHHKRZLWEHKDYHVLQWKHSUHVHQFHRI

ILGXFLDOPDUNHUV)RUWKLVDVLPXODWHGVFUHHQLPDJHZDVJHQHUDWHGXVLQJWKHVDPH

PHWKRGXVHGLQJHQHUDWLQJWKHVXQLPDJHDQLPDJHZDVJHQHUDWHGDWKLJKHUVFDOHDQG

WKHQVFDOHGGRZQWRWUXHVL]H3RUWLRQVRIWKLVVFUHHQZHUHWKHQ3LOOXPLQDWHG ́E\

PXOWLSO\LQJUHJLRQVRIWKHVFUHHQLPDJHZLWKWKHV\QWKHWLFVRODULPDJHJLYLQJWHVWLPDJHV

OLNHWKHRQHVKRZQLQWKHILJXUHEHORZ


Figure 13 Test image containing fiducial markers

7KHSDUDPHWHUVIRUWKLVEDWWHU\RIWHVWLQJDUHOLVWHGLQWKHWDEOHEHORZ7KHJRDOKHUHZDV

WRVHHKRZZHOOWKLVDOJRULWKPFDQKDQGOHHQFRXQWHULQJILGXFLDOPDUNHUV:KLOHFHUWDLQO\

QRWSHUIHFWFRPSDULQJWKLVWRWKHIOLJKWGDWDDWWKHVWDUWRIWKLVVHFWLRQVKRZVWKDWLWLVD

UHDVRQDEOHDSSUR[LPDWLRQRIZKDWWUXH3<$6LPDJHVORRNOLNH

Parameter Value

1RLVH6WG'HY FRXQWV

7KUHVKROG FRXQWV

1XPEHURI&KRUGV1 SHUD[LV

6XQFHQWHU DUFVHFRQGV

DUFVHFRQGV

%DFNJURXQG 2QHRIVXEVHWVRI

ILGXFLDOSDWWHUQ

7ULDOVSHUEDFNJURXQG 

Table 13 Parameters for test of sun-detection in the presence of fiducial markers

7KHUHVXOWVRIWKLVWHVWDUHWDEXODWHGLQWKHKLVWRJUDPRI566HUURUYDOXHVVKRZQEHORZ

5HFDOOWKDWWKHJRDOKHUHLVWRKDYHDQ566HUURUEHORZDUFVHFRQGV


Figure 14 Histogram of error levels for trials in the test of chord-based sun-detection in the presence 

of fiducial markers. Almost all tests fell within the 10 arcseconds requirement.

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ZKHUHWKLVDOJRULWKPIDLOVWRPHHWWKHUHTXLUHPHQW(YHQWKRXJKPRVWYDOXHVIDOOEHORZ

WKHWKUHVKROGWKHERXQGRQHUURUKHUHLVPXFKKLJKHUWKDQZKDWZDVVHHQLQWHVWVZLWKRXW

ILGXFLDOVSUHVHQW7KHUHDVRQIRUWKLVLVYLVLEOHLQWKHH[DPSOHIUDPHVKRZQDERYHDQG

ZDVRYHUORRNHGLQWKHSODQQLQJVWDJHVRIWKH3<$6FRGH/RRNLQJDWWKHWRSOHIWILGXFLDO

LQWKHVDPSOHLPDJHDERYHLWLVFOHDUWKDWLIDFKRUGZHUHWRIDOOKRUL]RQWDOO\DFURVVWKH

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RIWKHKRUL]RQWDODUPRIWKDWILGXFLDOZRXOGEHGHWHFWHGDVWKHHGJHRIWKHVXQZKLOHWKH

DFWXDOHGJHOLHVFORVHUWRWKHOHIWHGJHRIWKHPDUNHU7KLVFKRUGZRXOGLQWURGXFHDQ

RIIVHWDQGJLYHQWKDWWKHUHDUHRQO\FKRUGVDWPRVWWKURXJKWKHZKROHLPDJHRQHHUURU

FDQLQWURGXFHDVLJQLILFDQWSXOORQWKHHVWLPDWHRIWKHFHQWHU


 )LGXFLDO'HWHFWLRQ

 $UWLILFLDOILGXFLDOPDUNHUGDWDZDVGHVFULEHGEULHIO\LQWKHSUHYLRXVVHFWLRQZKHUHDQ

DUWLILFLDOILGXFLDOVFUHHQZDVXVHGWRWHVWWKHVXQWUDFNHU,QWKLVVHFWLRQUDWKHUWKDQWKH

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UHILQHPHQWPHWKRGGHVFULEHGLQ&KDSWHUFDQUHVROYHVXESL[HOORFDWLRQV

Figure 15 Example of a fiducial test image, and the corresponding correlation image

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YDULHGDFURVVGLIIHUHQWORFDWLRQVLQPLOVRQWKHILGXFLDOVFUHHQLQHDFKD[LV$OORI

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WKHPHWKRGWDNHQZLWKWKLVDOJRULWKP


No Refinement Centroid 

(FLIGHT)

Centroid

(Improved)

VLJPD566

HUURU

DUFVHFRQGV DUFVHFRQGV DUFVHFRQGV

Table 14 Performance of various fiducial location methods. Flight method is marked (FLIGHT), and 

an improvement which accounts for some of the systematic error is given as (Improved)

(UURUIRUWDNLQJQRDFWLRQLVZKDWZRXOGEHH[SHFWHGWKHHTXLYDOHQWRIDERXWKDOIDSL[HO

5HILQLQJWKHORFDWLRQRIWKHSHDNZLWKDFHQWURLGZDVDEOHWRFXWWKDWYDOXHLQKDOI

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ILWWLQJSUREOHP3DUDERORLGILWWLQJZRXOGKDYHEHHQWKHSUHIHUUHGDSSURDFKKHUHDQGZDV

VKRZQLQWKHOLWHUDWXUHWRSHUIRUPQHDUO\DQRUGHURIPDJQLWXGHEHWWHUWKDQWKHPHWKRG

FKRVHQKHUH7KHUHDVRQIRUSRRUSHUIRUPDQFHRIWKHFHQWURLGLVDV\VWHPDWLFHUURU

GHVFULEHGLQWKHJUDSKVEHORZ

Figure 16 At left, true fiducial locations are shown in black, all corresponding to the same integer 

pixel location. Attempts to refine fiducial location to sub-pixel are shown in red. Clearly there is 

systematic error present. At right, the same is shown for a single point.

 


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WKHUHVXOWLQJVROXWLRQDQGE\QRWVXEWUDFWLQJWKHWKUHVKROGWKH\DOVRKDYHPRUH3PDVV ́

7KHUHVXOWVRIVXEWUDFWLQJWKLVYDOXHZKHQFRPSXWLQJFHQWURLGDUHVKRZQEHORZ

Figure 17 Same as figure 16, but with an improvement on the method used on flight.

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5.3 Test Data

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 )LGXFLDOV

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Figure 18 Spread of fiducial locations from a test of the PYAS system

Figure 19 Fiducial location from a ground test, in a single dimension, plotted as a time series

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 5HJLVWUDWLRQ

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  Variance

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ɐ௠మ

ଶ PLOVSL[HO

ɐ௕భ

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ɐ௕మ

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ɐ୶

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Table 15 Measured noise values for parameters in the image registration stage

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5.4 Summary and Flight Performance

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Requirement Minimum Target Verification Result

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DUFVHFRQGV

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DUFVHFRQGV DUFVHFRQGV  

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Table 16 Summary of algorithm requirements and measured performance

 

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6.1 Ground Processing 

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