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### Analysis of Stray Light in a Brewer Spectrophotometer

Brewers are not Perfect!

C. A. McLinden, D. I. Wardle,

C. T. McElroy, &V. Savastiouk

Environment Canada

Stolen Stuff:

- David Wardle – many slides
- Tom Grajnar and Mike Brohart – data
- Volodya Savastiouk – many calculations…
- Jim Kerr – much code
- Chris McLinden - models

Brewer Workshop Beijing, China

Brewer Map

Brewer Workshop Beijing, China

MSC Toronto

Brewer Workshop Beijing, China

Mauna Loa Observatory

Brewer Workshop Beijing, China

EurekaWeather Station

Brewer Workshop Beijing, China

rationale

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.

Brewer Workshop Beijing, China

Dispersion and spectral purity…

- Given that we are to measure ozone from
- its UV spectrum, we need to know:
- 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.

Brewer Workshop Beijing, China

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

Brewer Workshop Beijing, China

The Brewer spectrophotometer optics

UV-vis

Diffraction grating: 1800 lines/mm

1st order: visible 570-650 nm

2nd order: UV 285-325 nm

Also: 1200 and 3600 lines/mm

turned by stepper motor

Brewer Workshop Beijing, China

Spectrometer layout

Brewer Workshop Beijing, China

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 S 1800 620 nm 2

Mark V S 1800 620 nm 2 1

Mark IV S 1200 1000 nm 3 2

Mark III D 3600 330 nm 1

Mark VI S 3600 330 nm 1

measuring: ozone NO2 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 .

Brewer Workshop Beijing, China

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. m2)

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.

Brewer Workshop Beijing, China

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.

Brewer Workshop Beijing, China

Slit #0 “slit function”

Brewer Workshop Beijing, China

Class I Single Brewers

Brewer Workshop Beijing, China

Class II Single Brewers

Brewer Workshop Beijing, China

Cass I SB - #017

Brewer Workshop Beijing, China

Class I - #s 007, 017, 109

Brewer Workshop Beijing, China

Extended Scan Singles #s 007, 109

Brewer Workshop Beijing, China

Three Single Brewers – 012, 014, 015

#014, #015

Are Toronto TRIAD

Instruments

Brewer Workshop Beijing, China

Double Brewers

Note: #085 scan was done before the replacement of the ground quartz

Brewer Workshop Beijing, China

Double Brewers using 353nm

Secondary peak at 325 nm is from impurity of the 353 nm laser

Brewer Workshop Beijing, China

325 & 352 nm laser scans ….

Brewer Workshop Beijing, China

325 & shifted 353 laser scans…

Brewer Workshop Beijing, China

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.

Brewer Workshop Beijing, China

The data

Brewer Workshop Beijing, China

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

Brewer Workshop Beijing, China

How to do laser scans

- Important: there must be no changes in the optical configuration or laser position when doing multiple ND filters

Brewer Workshop Beijing, China

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

Brewer Workshop Beijing, China

Ozone in Toronto - #s 085, 039

Brewer Workshop Beijing, China

Ozone at Sodankyla

Brewer Workshop Beijing, China

Airmass Dependence

…in the presence of an ETC error

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)

This is NOT what was happening in Sodankyla!

Brewer Workshop Beijing, China

Stray LightCorrection

Brewer Workshop Beijing, China

Brewer Workshop Beijing, China

CPFM on WB-57F

Brewer Workshop Beijing, China

CPFMStray LightFunction

Composition and

Photodissociative

Flux Measurement

Brewer Workshop Beijing, China

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 shoulder

Stray light wing

Brewer Workshop Beijing, China

Nature of Stray Light Effect

6

F = Σ al log[ Il ]

l=3

X = ( Fo – F ) / ( Δαμ )

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…

Brewer Workshop Beijing, China

Stray Light Simplified

Brewer ozone is based on slit positions l = 3 to l = 6

Sum over l = 4 to 6

β is stray light fraction

F = a3 log[ I3 + βI6 ] + Σ al log[ Il ]

F = a3 log[ I3 ( 1+ βI6/ I3 ) ] + Σ al log[ Il ]

F = Σ al log[ Il ] + a3 log[ 1+ βI6/ I3 ]

= F’ + a3 log[ 1+ βI6/ I3 ]

~ F’ + ζ I6/ I3 with ζ=a3β

Now X = ( Fo - F ) / ( Δα * μ )

l = 4 to l = 6

l = 3 to l = 6

Where F’ is the

true ozone ratio

Brewer Workshop Beijing, China

Rearranging

X = ( Fo - F ) / ( Δα * μ )

X = [ Fo – ( F’ + ζ I5 / I2) ] / (Δαμ )

= X’ - ζ I5 / I3 / ( Δαμ )

Now I3 = Io3 exp( - μα3 X’ )

X = X’ - ζ I5 * exp( μα3 X’ ) / Io2 / ( Δαμ )

For μα3 X’ small and I5 only lightly attenuated:

X ~ X’ - ζ Io5 * (μα3 X’ + (μα3 X’)2/2 ) / Io3 / (Δαμ )

X ~ X’ - ζ Io5/Io3 X’ - ζ Io5/Io3 μα3 X’2/2 since Δα ~ α3

X ~ X’ ( 1 - ζ Io5/Io3 - ζ Io5/Io3 μα3 X’/2 )

Let ξ = ζα3 / 2 and recognize that Io5 ~ Io3

X ~ X’ ( 1 - ζ - ξμ X’ )

X’ is the true ozone

Brewer Workshop Beijing, China

Stray LightCorrection

Brewer Workshop Beijing, China

- 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
- Deriving ETC by performing Langley on synthetic data
- Applying Brewer algorithm to synthetic data and ETC
- Stray light errors are determined by
- Modeling Brewer column including stray light
- Modeling Brewer column including only instrument function core
- Calculating fractional difference, (xstray – xcore) / xcore

Brewer Workshop Beijing, China

Modelled Fractional Stray Light Signal for Brewer #014

- Multiple latitudes and months (ozone profiles), SZAs considered
- (which is why there is some scatter)

Slit #

Brewer Workshop Beijing, China

Comparing Modelled Signals with Observations from Brewer #007 (Fairbanks, May 5, 2001)

- compare log(Si)-log(S5), where Si 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

Brewer Workshop Beijing, China

Modelled Stray light Error in Ozone Columns

Error () here caused primarily

by stray light wing; thus

(009)>(014)

Brewer Workshop Beijing, China

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)

Brewer Workshop Beijing, China

- 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

Brewer Workshop Beijing, China

Fitting a Lorentzian to the shoulder region and a constant to the wings seems reasonable (3 parameters)

#015

Brewer Workshop Beijing, China

Question: is a laserscan measured using slit 1 representative of stray light for slits 2-5?

Yes, although subtle

differences are evident when

examining Lorentzian

fitted parameters:

Slit Amplitude Width

(x10-3) (A)

1 5.05 13.4

2 5.26 12.9

3 5.84 12.8

4 5.73 12.6

Slit #

#015

Internal reflection

at Slit 5

Lorentzian Fits

Brewer Workshop Beijing, China

Correcting Brewer Measurements

Brewer equation with stray light can be written as

x = (F – F0 – 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 ai log(Si) where I = 1 to 5

F0 was calculated with stray light removed during the Langley analysis

Brewer Workshop Beijing, China

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

Brewer Workshop Beijing, China

The End – Thank you!

Brewer Workshop Beijing, China

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