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mtpanynuhnar>$mo$dahorpthnynur> $mi$am"m>//<$>$mo<$d$ye"m>//<$>$fue>$fivate>$paadimadAHeyxtdAagzerHHBCoHH5<$et` EHHBHH6` HUX
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1E11dA|HT%
B`Single LineEBHHBHH<_doppler data. For a 128x128 output grid, one can average 8x8 regions on CCD. This summation tis efficient, requiring about 128x128x64 operations, about 106 operations, or 2x106 cycles. It has $@inSthe disadvantage of significant spatial aliasing and is discarded for this reason.
7`ag(2.2 Low resolution 2-D Gaussian filter
J `A straightforward approach to observing up to some maximum low-l value could use a 2-D XinaGaussian filter on the observed Dopplergrams. This mode has the advantage of observing the full Ef^solar disk. It has the disadvantage of requiring significant computation (for 120x120 output tBipixels, requires of the order of 32x32 operations per output pixel, or about 1.5x107 operations, @5perhaps 30x106 cycles, or nearly 3 seconds).
h!See Figure 1 for an outline.
oX 1lIn addition, due to projection effects, a Gaussian average optimised for l =120 at disk center will , f8xsonly reach l = 60 at a latitude of 60 degrees. So to reach l = 120 on the disk (say out to 60) ntatsp`requires a finer grid and hence more telemetry. Alternatively, varying resolution 2-D Gaussian Ga@5filters could be used (this was deemed impractical).
n%;&C e mequal[char[nu],times[over[num[1,"1"],times[num[2,"2"],char[pi]]],sqrt[over[times[char[g],char[l]],char[R]]]]]e&4qC Iequal[over[indexes[0,1,char[l],times[char[m],char[a],char[x]]],num[3,"3"]],over[indexes[0,1,char[m],times[char[m],char[a],char[x]]],num[3,"3"]]]tidAx1} HHB0HH<`reOutline of Gaussian Mask Mode
0`#dd(Peter N. Milford and Philip H. Scherrer
anTh# f
30 January 1992
ex`#SOI-TN-058
sonUT UT` 1. Introduction
o tooTo maintain a uniform dataset of modes for analysis, complete coverage of all l and m, up to e t@tiosome l$max is desireable. This mode set can also be used for comparison with other observations.
.
n CqThe objective of the Gaussian mask mode is to measure solar oscillations for all l and m up to carwsome limit (about l$max = 120). It need not do well on very low-l, as this is covered by the LOI ]]]@inobserving mode.
ti ],|The high-l limit is set by choosing the maximum l for which we want all m (within the constraint ]of the telemetry). The value 120 is selected as being about where there is temporal overlap d* a\between adjacent modes; e.g., because there is spatial leakage between nearby modes, if the SO8UT`modes are not sufficiently well separated in frequency then the modes will overlap in frequency naF@veMspace, taking their lifetimes into account, and the modes blend into ridges.
lY`esS(The frequency spacing of adjacent ls can be approximated by (for f-mode):
{hTh
thn
d`la
s` ~at l of 50, dn ~ 7mhz; typical FWHM ~ 2 mhz, and overlapping adjacent modes can be resolved.
thwat l of 120, dn ~ 4.5 mhz, and FWHM ~4 mhz (?) and overlapping adjacent modes are not t b@im
resolved.
t iSomewhere in the l ~ 120 range the modes blend together to form ridges. The goal is to measure retall l and m for which the oscillation can be treated as isolated modes. Due to telemetry limits, en"@ththis goal may be compromised.
KUR UT`ly2. Possible Approaches
ncyc`ll2.1 Boxcar Averages (PTO)
v spiThe simplest method of obtaining lower-l data is by taking boxcar averages of the full disk CCD uR49=\!bKGs
D (NN KCTh(kHyequal[over[times[char[delta],char[nu]],times[char[delta],char[l]]],times[over[num[1,"1"],times[num[4,"4"],char[pi]]],sqrt[over[char[g],char[R]]],over[num[1,"1"],sqrt[char[l]]]]]b kP$1$Gat
D&SqC ~*(?equal[cross[indexes[0,1,char[l],times[char[m],char[a],char[x]]],over[indexes[0,1,char[l],times[char[m],char[a],char[x]]],num[3,"3"]]],comma[num[15,"15"],num[0,"000"]]]m r]'=w6qG %!
DdAth~re'=wU&qG le %!
DHHBprHH<Ap
es`2.3 Remap Gaussian Filter
O)
sp_An alternate approach is to compute 2-D Gaussian averages on the already remapped image. This di)\dhas the advantage that the effects of the geometric projection have been removed, so a constant set eq7r[gof 2-D Gaussian filters can be used (for output linear in sine latitude and in longitude) - see Figure chaEr[e2 - or a varying set of 2-D Gaussian filters, which vary only in latitude, can be used for an output qS@ ~"linear in latitude and longitude.
f s[^The APU cycles required for this calculation are about the same as for the low resolution 2-D t@,nGaussian filter mode.
aThis mode has the disadvantage of using the remapped data: only partial disk data, and slightly HMnoisier data after the remap. The telemetry stream is fitted optimally.
]`2.4 Gaussian Mask Mode
p RcIn the remap Gaussian filter, one dimension of the filtering is in the E-W direction, but the next es ~apdstep in the structure program processing is a Fourier transform along rows (of constant latitude). onHA seH!
ficaUUh
puNote: this is really (l-m)!max
; we get all l
and m
up to l!max"
and all l,m
for
.Â7'G n 8
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'C cۃ' aYleq[id[plus[char[l],minus[char[m]]]],indexes[0,1,char[l],times[char[m],char[a],char[x]]]]dAe thHHBk HH<<!<no
da. \Filtering in the E-W direction in the Fourier domain can be done by discarding the higher Rhfrequency components. For m = 120, we take data from the first 40 columns (complex data); each $@stgcolumn is labeled by 3m. This gives all l for m up to 120. See Figure 3.
7 \The columns can now be either processed with a Gaussian-like mask to produce low resolution s E!hdata linear in latitude or in sine latitude. To produce data linear in sine latitude requires only one S^Gaussian mask, with around 30 - 60 non-zero elements. It is used 120 times on each (complex) a@Ccolumn of data:
ۃt`idUTotal operations 120x40x2x60 = 0.6 million, or about 1.2 million cycles.
eAlternately, masks can be constructed to remap the data to be linear in latitude. There will be 120 !Hda2different masks then, of about the same size.
)HHHH b d5V11H8#Hor"`&Je rs"#H `J bed #REZ
ɹ J
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INPUT DATAY
ɹ
J ocbbi1024k L8aaJ
m
ɹJ
udmm 1024duh
ɹ
Jquqq120E
ɹJ
0 EE 120s u-7QZ
ɹJ-@-@nOUTPUT DATAt<J Jorboy`Je ns``yineJ !y th<1J<115<
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ɹMkkNT k1
ɹMkkFWHM~8$1
ɹM--JFWHM~8m{'
ɹM10mmJFILTERJ@
ɹM12??JFigure 1: 2-D Gaussian Filter(+KJz~+ ٨?^RQ{F.d`)@r >ZBJ";
D<(+K<FW}tqlmE?F< >d A!!HH!B HH< UT UT`3. Precision
!`3.1 Mask Precision
U4 `By analogy with POX masks: 8 bits, as the masks are so small (either one 60-element mask or 120 B@P60-element masks) they may as well be stored and represented as 16-bit numbers.
ɹZ`3.2 Data precision
m _By analogy with POX data: 8 bits. Alternately, the Fourier transformed data is about 8-9 bits {@FIJprecision, we average over about 16 elements, so output data is ~11 bits.
UR UT`r'4. High Resolution Gaussian Mask Mode
[Prior to the POX masks being loaded, the Structure Program operates in the high resolution @ZGaussian mask mode, identical to the Gaussian mask mode, but with data at a higher-l.
// ZThere is enough telemetry for about 30,000 8-bit numbers, or 15,000 complex numbers. To hl\zcalculate the maximum l,
that there is telemetry for, there are l$max points in the N-S direction % %na_and
in the E-W direction, so
or l$max = 212 and the data is zS/@le212x70 complex numbers.
l* rejIf the data compresses better: then we can send 60,000 numbers for l$max = 300 for a 300x100 8@. raster.
ly`jF UT`sf+5. Compression of Gaussian Mask Mode Data
@y e XThe Gaussian mask mode data should compress reasonably well in the N-S direction (along R@ MPcolumns), probably about the same as velocity data - use Rice compression only.
rejD UT`in76. Selection of Linear Sine Latitude or Latitude Grid
sk jB UT` t7. Mask Generation
b hi[The masks are generated on the ground and uplinked (with IP memory load commands). In the or @beblinear in sine latitude mode, the mask is a Gaussian, truncated to about 30-60 non-zero elements.
`)7.1 High Resolution Gaussian Mode Masks$"Q"K#on,
B
ɹ#K"$ 2
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ɹ$K#%exII
Input data?^
ɹ%K$&weHHs#Sine(lat) (Remapped Dopplergram)00xAuPP
ɹ&K%(lyA~A~.1024 (longitude)aug
ɹ'K56ggmk +ջQQ(J&)lywelUP)J(*UUUabo@ջQ*J)+ Re @ջ@ջU`kջP*E+J*, LitkջkU,UQ,J+-,U}UUate*UQ-J,. Ime*U{UU-UQ.J-/atud-U~UUrun3U@/M.0en.
3UsUUeso;&
ɹ0M/1;U;U:&1
ɹ1M02:U:UFWHM~9&1
ɹ2M13UUFWHM~8@&'
ɹ3M24@U@UFILTER)ݻK4K35am0x&ݻq% 9)
ͻ)ݻ"Ktud*NP#5K4'*:՞J2N\{`g{p]4{&*CPyb.<]A6K'7WDN@
ɹ7K68ջ``Sine (latitude)@Q+
ɹ8K79Q4Q4L120kX
ɹ9K8:aa120D1S
ɹ:K9;DDJ Longitudex
ɹ;K:xxFigure 2: Remap Gaussian Filter~Z<B=_
Den'"lH=K><eso9"H>K=@<9"9j1'El?KCE<U'EE2MK"H@K>B<K"Kjo#HAKBC<FIERo#okBam]"HBK@A<%]"]j0K#HCKA?<#kT`@
ɹDKFG<II900'7'WlEK?F<K8'WW%&4lFKED<ɹK&44&
ɹGKDH<:&&0Input data (Result of Fourier transforms on ---)?DN@
ɹHKGI<itHHKSine (latitude)x(v#IMHJ<maGa(vKv<B,w
ɹJMIK<D,,K40UmC
ɹKMJL<KUvUv512 ComplexUy4
ɹLMKM<KUU
3mKpoMKLN<KBKpoKp~P*$?[NKMO<KCU*PUt[^*XaܰX#WբT^*[@Anv{1
ɹOKNP<nvĪnvĪFWHM~8Ao{/
ɹPKOQ<AoAo
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ɹQKPS<1*S1*SOutput DataEK(kT
ɹRK[\<(k]+
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120l?B&rHlSKQT<@o*HTKSU<ɹ@o*o*79*@*\HUKTV<urr @*\*\7*&
ɹA*JHVKUW<A*J*J8*#@=9*HWKVX<@=9*=9*7=*O>'*lXKWY<O>*O>'*>+*JLbC'*lYKXZ<51bC*bC'*C+*KM@**HZKY[< @****7*K*LNtE'l[KZR<tEtE'#E+MOCQP8R
ɹ\KR]<[CjCj
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1-$QVI
ɹ_K^<$p$pS"Figure 3: Remap Gaussian Mask ModeHZ`Gk
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