Mars Data Analysis Using IDL GG7101 Lecture 12

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Mars Data Analysis Using IDLGG710-1Lecture 12

• F. Scott Anderson
• Office POST 526B
• Phone [phone]
• Email anderson_at_higp.hawaii.edu

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Review of 11/10/04

• Finish Graphics
• Shaded surface plots, large images
• Copying a screen image
• Reading and writing graphics files
• Other devices postscript and z-buffer
• Maps
• Useful math functions in IDL
• Curve Fitting
• Polynomial least square fits
• Minimum absolute deviation fits

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Today

• Homework graded
• Questions from last time
• Quiz 10
• Useful math functions in IDL
• FFT's
• Review of today's class

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Questions from 11/8/04

• Squeaky wheels, Troublemakers, Forever Hold your
  piece?

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Quiz 9/10 Scores
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Quiz 10
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Quiz Answers
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Quiz Answers
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SPD-TEST Homework

• pro spd
• nn100 res1fltarr(nn) res2fltarr(nn)
  res3fltarr(nn)
• for ctr0, (nn-1) do res1ctrspd1()
• for ctr0, (nn-1) do res2ctrspd2()
• for ctr0, (nn-1) do res3ctrspd3()
• plot, res1, yrange0.04, 3, /xstyle,
  /ystyle, /ylog,
• ytitle'Time (s)', xtitle'Test',
  title'Efficiency test'
• oplot, res2, psym-2 oplot, res3, line3
• oplot, 5, 15, 0.8, 0.8
• oplot, 5, 15, 0.7, 0.7, psym-2
• oplot, 5, 15, 0.61, 0.61, line3
• xyouts, 20, 0.8, string('Avg. Time ',
  strtrim(mean(res1), 2))
• xyouts, 20, 0.7, string('Avg. Time ',
  strtrim(mean(res2), 2))
• xyouts, 20, 0.61, string('Avg. Time ',
  strtrim(mean(res3), 2))
• end

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TES Answer

• Use SIS to determine units of radiance in data
  file W cm-2 st-1 wvn-1 W/cm
• Plug in MKS values into three equations provided
  and determine which has the same units as
  radiance above
• Wavenumber Eqn 4.3
• Could use other equation, but must convert answer
  to wavenumber units before finishing
• Rewrite equation for T Tf(LB, n)
• Read file, get n and L

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TES Answer

• Calculate T for each L as f(n) 143 values
• Use Method.txt to derive surface T
• First calculate T as f(e)
• TB (Assumed e 1.0)
• TB' (Assumed e-0.97)
• Tf(LB, n) Eqn 4.3 rewritten
• From notes, e LBL
• Thus, LBL/ e
• Thus, Tf(L/ e, n)
• Find max from 300-500 800-1350
• Note that max(TB)gt225 gt Tsurfacemax(TB)

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TES Answer

• Now that we have one final "real" temperature
• Calculate emissivity
• Calculate predicted radiance (planck) curve for
  Tsurface
• Divide observed radiance by predicted radiance
• Plot wave vs T
• Exclude left axis
• Add axis for e
• Plot wave vs e

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TES Homework
6
Temperature
Emissivity
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TES Homework
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Hematite!
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Code

• function planck_wvn_t2r, t, wvn
• t1double(t) wvn1double(wvn)
• h6.625D-34 Js
• k1.381D-23 J/k
• c2.998D8 m/s
• L1 2Dhc2wvn13
• L2 exp(hcwvn1/(kt1))-1
• L L1/L2
• return, reform(L)
• end

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Code

• function planck_wvn_r2t, r, wvn
• r1double(r) wvn1double(wvn)
• h6.625D-34 Js
• k1.381D-23 J/k
• c2.998D8 m/s
• L1 hcwvn1/k
• L2 alog(2Dhwvn13c2/r11)
• T L1/L2
• return, reform(T)
• end

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Code

• function calc_surf_t, brt1, brt2, wvn
• T1 215 T2 225 s1(((wvn ge 300) and
  (wvn le 500))
• s2((wvn ge 800) and (wvn le 1350))
• subs1 where(s1 or s2)
• mbt1 max(smooth(brt1subs1,7,/edge_truncate
  )) TB
• mbt2 max(smooth(brt2subs1,7,/edge_truncate
  )) TB'
• if (mbt1 ge T2) then Tsurface mbt1
• else if (mbt2 le T1) then Tsurface mbt2
  
• else begin
• wgt1 1 - ( (T2 - mbt1) /
  (T2-T1) )
• if (wgt1 lt 0.0) then wgt1 0.0
• wgt2 1 - ( (mbt2 - T1) /
  (T2-T1) )
• if (wgt2 lt 0.0) then wgt2 0.0
• Tsurface ( (mbt1wgt1)
  (mbt2wgt2)) / (wgt1wgt2)
• endelse
• return, Tsurface
• end

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Code

• pro tes
• aread_ascii('TES_data.txt', data_start5)
• wvna.field10, Wvn in 1/cm
• rada.field11, Rad in W cm-2 sr-1
  wvn-1
• W
  cm-2 sr-1 cm
• W
  1/cm sr-1
• Variables for graph range
• min_wvn200.0 max_wvn1301.0
• wvn1wvn1e2 Convert wvn to 1/m
• rad1rad1e2 Convert rad to 1/m
• wvl1e4/wvn Wavenumber in um

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Code

• Calculate brightness temperature from
  radiance for e1.0 and e0.97
• brt1 planck_wvn_r2t(rad1, wvn1)
• brt2 planck_wvn_r2t(rad1/0.97, wvn1)
• Calculate the surface temperature
• Tsurface calc_surf_T(brt1, brt2, wvn)
• Calculate the final planck curve using the
  surface temperature
• all calculations in 1/m (mks) so must
  convert to 1/cm
• rad1 planck_wvn_t2r(Tsurface, wvn1)/1e2

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Code

• Plot the graph
• plot, wvn, brt1, xrangemax_wvn, min_wvn,
  yrange255,280,
• charsize2, xtitle'Wavenumber
  (cm!U-1!N)',
• ytitle'Temperature (K)',
  ymargin3.5,3, xstyle9,
• ystyle9, xmargin7,7
• Add an emissivity y axis
• axis, yaxis1, yrange0.76, 1, /ystyle,
  ytitle'Emissivity',
• charsize2,/save
• Plot the emissivity for this spectrum
• oplot, wvn, rad/rad1
• end

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Mini-Homework

• My Favorite Projection

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Mini-Homework Answer

• pro map_mars
• read_jpeg,'mgstopo3.jpg',a
• map_set, -5, 120, /satellite,
  sat_p1.1,0,0,/iso, /noborder
• rmap_image(reform(a0,,), x0, y0, xs, ys,
  compress1)
• gmap_image(reform(a1,,), x0, y0, xs, ys,
  compress1)
• bmap_image(reform(a2,,), x0, y0, xs, ys,
  compress1)
• imgfltarr(3,xs,ys)
• img0,,r img1,,g img2,,b
• tvscl, img, /true
• end

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Fourier Transform

• Concept Any data can be approximated by the
  summation of some number of sine and cosine waves

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Fourier Transform

• A FT identifies what l's are in dataset
• Transforms from space or time to l
• Every possible l of sine or cosine will have
• Amplitude
• Non-zero values indicate the l exists in data
• Phase shift

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Basics l, n
n 1 / l
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Wave Basics

• These waves have amplitude of 1
• Cosine and Sine are the same shape shifted by 90
• Thus, 2nd wave is same as first with 90 shift

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Fourier Convolution

• A FT takes multiple steps
• First it loops over every possible l
• For each l it loops over every possible phase
• The FT takes each possible combination of l
  phase, and multiplies it against the observed
  data
• The amplitude of the correlation is the amplitude
  of the result

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Discrete Waves Nyquist n

• Because waves in IDL are made of discrete points,
  there are a limited number of l phase possible
• Largest wave that can be uniquely distinguished
  over N points is just the length of the data
• Smallest wave is N / (2 len)
• Thus, N/2 cosines, N/2 sines total of N
  possible waves
• Similarly, there are N possible phases
• N2 possible combinations
• FFT uses tricks to solve for even fewer
  combinations

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Fourier Transform

• A FT of a vector will result a vector of the same
  length in which
• The values are the amplitude phase for each
  wave (a set complex numbers)
• The position of each value indicates it's l
• Are we getting back more numbers than we gave
  FFT?
• FFT(Vector with n values) gt
• Complex vector of n x 2 Values!
• But 1/2 of the returned values are redundant

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Fourier Transform

• If you have a vector of amplitudes in positions
  corresponding to l can invert back to original
  data using inverse fourier transform (IFT)
• FFT(spatial/temporal data) gt l
• IFT(l) gt Spatial/Temporal Data

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Fourier Transform

• Who cares? Why identify l's in a dataset?
• Filtering
• Not unusual to have noise at some l but not
  others
• Low pass (screens out high frequency noise -
  static)
• High pass (screens out low frequency noise - slow
  drift)
• Data manipulation
• Physics of wave damping (seismic, gravity) e-kz
• Relationship for specific l TlClgl
• Power spectra
• Sometimes want to know what l dominates data

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IDL's FFT

• Form FFT
• ResultFFT(Array)
• Form IFT
• ResultFFT(Array, /inverse)
• Frequency of each value in the result array is
• Odd pts
• Even

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Simpler n Order

• Odd pts
• Even
• Easier to remember
• Follow mathematical definition

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FFT Steps

• Obtain data (need to know length amplitude)
• Calculate shifted frequency of each position in
  result array
• Calculate shifted FFT
• Plot!

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Calculating n , FFT

• To calculate shifted frequency
• f(findgen(nn)-(round(nn/2.)-1))/len
• To calculate FFT
• vshift(fft(y), round(nn/2.)-1)
• To calculate phase must convert to degrees
• faatan(v,/phase)/!DTOR

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Results Cosine Amplitude
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Results Cosine Phase
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Results Sine Amplitude
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Results Sine Phase
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Results 2 Cosines
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Results Cosines Sine
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Power Spectrum

• A power spectrum is defined as
• The positive side of the frequencies
• P 2ABS(Complex Amplitude)2

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Today

• Quiz 8 returned/Quiz 9 given
• Homework Review
• Mini-Homework Review
• FFT's
• Power Spectra

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Next Time

• GUI's
• Event Loop Concept
• Widgets
• Compound Widgets
• Widget ID's
• Event Structures
• Checking Events in the Event Loop