1. Analysis of Stray Light in a Brewer Spectrophotometer C. A. McLinden, D. I. Wardle, C. T. McElroy, &V. Savastiouk Environment Canada Brewers are not Perfect!

2. 31 May – 3 June 2005Brewer Workshop Beijing, China2 Stolen Stuff: David Wardle – many slides Tom Grajnar and Mike Brohart – data Volodya Savastiouk – many calculations… Jim Kerr – much code Chris McLinden - models

3. 31 May – 3 June 2005Brewer Workshop Beijing, China3 Brewer Map

4. 31 May – 3 June 2005Brewer Workshop Beijing, China4 MSC Toronto

5. 31 May – 3 June 2005Brewer Workshop Beijing, China5 Mauna Loa Observatory

6. 31 May – 3 June 2005Brewer Workshop Beijing, China6 Eureka Weather Station

7. 31 May – 3 June 2005Brewer Workshop Beijing, China7 Global column ozone: Develop confidence in prediction of the future (ozone); models are tuned to reproduce currently measured amounts, also to reproduce measured values during past 20 years. Target accuracy 1.0% 2-sigma. (or maybe 2 or 3 DU) Reasonable to have 20-50? instruments deployed over the world using the measurements with those from space instruments. Over the last 20 years we have almost achieved 1.0% RMS for daily average measurements with our best 3 instruments in Toronto. rationale

8. 31 May – 3 June 2005Brewer Workshop Beijing, China8 Dispersion and spectral purity… Given that we are to measure ozone from its UV spectrum, we need to know: (a)accurately the wavelengths of the measurement; in fact if the wavelength uncertainty is less than 0.01nm it is ok. if >0.02nm, it is a problem. Thus we need δλ/λ ~ 1/30,000. (b)that the much stronger radiation at longer wavelengths is not interfering with the measurement.

9. 31 May – 3 June 2005Brewer Workshop Beijing, China9 Spectrometer The idea is to have monochromatic light at the exit slit Diffraction grating is used to separate different wavelengths and send them at different angles

10. 31 May – 3 June 2005Brewer Workshop Beijing, China10 UV-vis turned by stepper motor Diffraction grating: 1800 lines/mm 1 st order: visible 570-650 nm 2 nd order: UV 285-325 nm Also: 1200 and 3600 lines/mm The Brewer spectrophotometer optics

11. 31 May – 3 June 2005Brewer Workshop Beijing, China11 Spectrometer layout

12. 31 May – 3 June 2005Brewer Workshop Beijing, China12 Spectrometer Gratings and “Marks” Brewer gratings all have the same dispersion in the UV determined by n/d = 3600 lines per mm * order Usually as follows: ---- order in ----- Grating pitch Blazed for UV BLUE RED Mark II S1800 620 nm 2 Mark V S1800 620 nm 2 1 Mark IV S1200 1000 nm 3 2 Mark III D3600 330 nm 1 Mark VI S3600 330 nm 1 measuring: ozone NO 2 ozone at low sun Mark III is a double spectrometer (D); roughly the same transmission characteristics as the singles (S), except for “stray light”. Another variation is that earlier Brewers have a much smaller Slit#0.

13. 31 May – 3 June 2005Brewer Workshop Beijing, China13 Some dogma……………… For a single wavelength input to a linear spectrometer we can write Signal = intensity of input * f( ,  s ) where  is the wavelength of the input radiation &  s is the wavelength setting. f( ,  s ) is a response function (count rate. W-1. m 2 ) note: the dispersion function is  s = G( steps ) We often do a line scan in which we use a constant input , and vary the setting  s. What is more relevant is changing the input given a constant setting. We’ve looked principally at two types of line scan file, c. 9000 from spectral lamps, c. 200 from HeCd Lasers.

14. 31 May – 3 June 2005Brewer Workshop Beijing, China14 Dogma continued……………… For a spectrum of input radiation: Signal(  s ) =  P(  ) * f( ,  s ) * d  Where P(  ) is the spectral irradiance (watts m -2 nm -1 ) Most spectrometer users assume the above can be simplified to: Signal(  s ) =  P(  )*R(  s )*q(  -  s )*d  R may be called the responsivity and q the “slit function,” and q(  ) normalized to 1. i.e.:  q(  ) d  == 1.0 …..Not entirely correct.

15. 31 May – 3 June 2005Brewer Workshop Beijing, China15 Slit #0 “slit function”

16. 31 May – 3 June 2005Brewer Workshop Beijing, China16 Note the log scale! How do Brewers Compare??

17. 31 May – 3 June 2005Brewer Workshop Beijing, China17 Class I Single Brewers

18. 31 May – 3 June 2005Brewer Workshop Beijing, China18 Class II Single Brewers

19. 31 May – 3 June 2005Brewer Workshop Beijing, China19 Cass I SB - #017

20. 31 May – 3 June 2005Brewer Workshop Beijing, China20 Class I - #s 007, 017, 109

21. 31 May – 3 June 2005Brewer Workshop Beijing, China21 Extended Scan Singles #s 007, 109

22. 31 May – 3 June 2005Brewer Workshop Beijing, China22 Three Single Brewers – 012, 014, 015 #014, #015 Are Toronto TRIAD Instruments

23. 31 May – 3 June 2005Brewer Workshop Beijing, China23 Note: #085 scan was done before the replacement of the ground quartz Double Brewers

24. 31 May – 3 June 2005Brewer Workshop Beijing, China24 Secondary peak at 325 nm is from impurity of the 353 nm laser Double Brewers using 353nm

25. 31 May – 3 June 2005Brewer Workshop Beijing, China25 325 & 352 nm laser scans ….

26. 31 May – 3 June 2005Brewer Workshop Beijing, China26 325 & shifted 353 laser scans…

27. 31 May – 3 June 2005Brewer Workshop Beijing, China27 325 & 353 nm comments……… So yes the shape is the same, or is it? Actually the centre is ~10% narrower as the optics dictate has ~10% less energy wings are ~20% lower have ~20% less energy The reasoning is that the ratio of good to bad should be constant regardless of slit width, assuming the aberration-and-diffraction- determined width is smaller than the geometrical (slit-size- determined) width, which appears to be the case.

28. 31 May – 3 June 2005Brewer Workshop Beijing, China28 The data

29. 31 May – 3 June 2005Brewer Workshop Beijing, China29 How to do laser scans Need to do at least at two neutral density filter wheel positions to capture both the peak and the “stray light” It looks like we can use laser scans to find neutral density factors for the single instruments, but not for the doubles. Need to characterize the ND filters separately for the doubles

30. 31 May – 3 June 2005Brewer Workshop Beijing, China30 How to do laser scans Important: there must be no changes in the optical configuration or laser position when doing multiple ND filters

31. 31 May – 3 June 2005Brewer Workshop Beijing, China31 Conclusion We are learning a great deal about the Brewers with laser scans We need to help Tom and Mike with establishing rules on how to do laser scans in the field We also need to propagate this information to the rest of the Brewer community

32. 31 May – 3 June 2005Brewer Workshop Beijing, China32 Ozone in Toronto - #s 085, 039

33. 31 May – 3 June 2005Brewer Workshop Beijing, China33 Ozone at Sodankyla

34. 31 May – 3 June 2005Brewer Workshop Beijing, China34 Airmass Dependence x = ( Fo - F ) / ( alpha * mu ) …with dFo the error in ETC… x’ = ( Fo + dFo - F ) / ( alpha * mu ) = x - dFo / ( alpha * mu ) %x = x - [ x + dFo / ( alpha * mu ) ] / x * 100 = - dFo / ( alpha * mu ) / x * 100 let sx = mu * x slant column ozone %x = %x( mu = 1 ) / mu So at 2400 DU more we expect a 1%(mu = 0) to be 1% / 6 = 0.15% (mu=6) …in the presence of an ETC error This is NOT what was happening in Sodankyla!

35. 31 May – 3 June 2005Brewer Workshop Beijing, China35 Stray Light Correction

36. 31 May – 3 June 2005Brewer Workshop Beijing, China36 Courtesy A. Cede

37. 31 May – 3 June 2005Brewer Workshop Beijing, China37 CPFM on WB-57F

38. 31 May – 3 June 2005Brewer Workshop Beijing, China38 CPFM Stray Light Function Composition and Photodissociative Flux Measurement

39. 31 May – 3 June 2005Brewer Workshop Beijing, China39 Single-Brewer stray light rejection is 10 -5 -10 -4 as measured by scanning 325 nm HeCd laserline Instrument function core, FWHM=0.55 nm Stray light wing Stray light shoulder Laserscans

40. 31 May – 3 June 2005Brewer Workshop Beijing, China40 Nature of Stray Light Effect 6 F = Σ a l log[ I l ] l=3 X = ( F o – F ) / ( Δα μ ) Stray light adds signal at each wavelength. largely from longer wavelengths (spectrum gradient) Assume that the stray light is from the longest wavelength, and affects the shortest the most…

41. 31 May – 3 June 2005Brewer Workshop Beijing, China41 Stray Light Simplified F = a 3 log[ I 3 + βI 6 ] + Σ a l log[ I l ] F = a 3 log[ I 3 ( 1+ βI 6 / I 3 ) ] + Σ a l log[ I l ] F = Σ a l log[ I l ] + a 3 log[ 1+ βI 6 / I 3 ] = F’ + a 3 log[ 1+ βI 6 / I 3 ] ~ F’ + ζ I 6 / I 3 with ζ=a 3 β Now X = ( F o - F ) / ( Δα * μ ) Brewer ozone is based on slit positions l = 3 to l = 6 Sum over l = 4 to 6 β is stray light fraction Where F’ is the true ozone ratio l = 4 to l = 6 l = 3 to l = 6

42. 31 May – 3 June 2005Brewer Workshop Beijing, China42 Rearranging X = ( F o - F ) / ( Δα * μ ) X = [ F o – ( F’ + ζ I 5 / I 2 ) ] / (Δαμ ) = X’ - ζ I 5 / I 3 / ( Δαμ ) Now I 3 = I o3 exp( - μ α 3 X’ ) X = X’ - ζ I 5 * exp( μ α 3 X’ ) / I o2 / ( Δαμ ) For μ α 3 X’ small and I 5 only lightly attenuated: X ~ X’ - ζ I o5 * (μ α 3 X’ + (μ α 3 X’) 2 /2 ) / I o3 / (Δαμ ) X ~ X’ - ζ I o5 /I o3 X’ - ζ I o5 /I o3 μ α 3 X’ 2 /2 since Δα ~ α 3 X ~ X’ ( 1 - ζ I o5 /I o3 - ζ I o5 /I o3 μ α 3 X’/2 ) Let ξ = ζ α 3 / 2 and recognize that I o5 ~ I o3 X ~ X’ ( 1 - ζ - ξ μ X’ ) X’ is the true ozone

43. 31 May – 3 June 2005Brewer Workshop Beijing, China43 Stray Light Correction

44. 31 May – 3 June 2005Brewer Workshop Beijing, China44 Stray light is modelled by 1.Calculating transmitted solar irradiances from 290-350 nm at 0.05 nm resolution, multiplying by measured responsitivity, and convolving with laser scan to get synthetic Brewer measurements for each slit 2.Deriving ETC by performing Langley on synthetic data 3.Applying Brewer algorithm to synthetic data and ETC Stray light errors are determined by 1.Modeling Brewer column including stray light 2.Modeling Brewer column including only instrument function core 3.Calculating fractional difference, (x stray – x core ) / x core

45. 31 May – 3 June 2005Brewer Workshop Beijing, China45 Modelled Fractional Stray Light Signal for Brewer #014 -Multiple latitudes and months (ozone profiles), SZAs considered (which is why there is some scatter) Slit #

46. 31 May – 3 June 2005Brewer Workshop Beijing, China46 Comparing Modelled Signals with Observations from Brewer #007 (Fairbanks, May 5, 2001) -compare log(S i )-log(S 5 ), where S i is signal at slit i -Small differences may remain due to assumed Rayleigh, solar flux, slit widths; slit 0 and 1 suggest slightly too much stray light in model i=4 i=3 i=2 i=1 i=0

47. 31 May – 3 June 2005Brewer Workshop Beijing, China47 Modelled Stray light Error in Ozone Columns Error (  ) here caused primarily by stray light wing; thus  (009)>  (014)

48. 31 May – 3 June 2005Brewer Workshop Beijing, China48 Modelled Stray light Error in Ozone Columns ** Model predicts non-zero error even for small slant columns Error (  ) here caused primarily by stray light shoulder; thus  (014)>  (009)

49. 31 May – 3 June 2005Brewer Workshop Beijing, China49 Modelled Stray light Error -Non-zero error at small  x is at 1-1.5% level -Jim Kerr (personal communication) estimated this to be about at ~1% error by analyzing Brewer measurements -A small model-measurement inconsistency may remain

50. 31 May – 3 June 2005Brewer Workshop Beijing, China50 Parameterizing Laserscans Fitting a Lorentzian to the shoulder region and a constant to the wings seems reasonable (3 parameters) #015

51. 31 May – 3 June 2005Brewer Workshop Beijing, China51 Parameterizing Laserscans Question: is a laserscan measured using slit 1 representative of stray light for slits 2-5? Internal reflection at Slit 5 #015 Yes, although subtle differences are evident when examining Lorentzian fitted parameters: SlitAmplitudeWidth (x10 -3 ) (A) 15.0513.4 25.2612.9 35.8412.8 45.7312.6 Slit # Lorentzian Fits

52. 31 May – 3 June 2005Brewer Workshop Beijing, China52 Correcting Brewer Measurements Brewer equation with stray light can be written as x = (F – F 0 –  F) /  where  F is the stray light contribution to F (that is, subtracting  F from F removes the stray light), and is a combination of the fraction of stray light at slits 2, 3, 4, and 5  F (calculated in the model) for a particular Brewer can be expressed as a combination of the signals (S) at each slit  F =  i a i log(S i ) where I = 1 to 5 F 0 was calculated with stray light removed during the Langley analysis

53. 31 May – 3 June 2005Brewer Workshop Beijing, China53 Correcting Brewer Measurements After applying parameterization of  F to model columns, remaining stray light error is <2 DU for SCD up to 4000 DU. #015

54. 31 May – 3 June 2005Brewer Workshop Beijing, China54 The End – Thank you!