Brewer Ozone Spectrophotometer Mechanical Design Principles #2. C.T. McElroy York University Canada

Transcription

1 Brewer Ozone Spectrophotometer Mechanical Design Principles #2 C.T. McElroy York University Canada

2 Optics of the Brewer Spectrophotometer A Little History Fore-optics (1, 2) Spectrometer layout Grating angles and pitch Focusing the spectrometer Ebert and Brewer aberrations - general Transmission function definitions Aberration widths, Brewer Aberration widths, Brewer versus Ebert Ray-traced transmission function statistics Ray-traced transmission functions Post-spectrometer optics Field and aperture stops Appendix: spectrometer dimensions 2

3 Fore-optics (1) UV Port = diffuser + prism. Iris: image of sun or sky Entrance slit: image of sky or sun L 2 L 3 L 4 f 2 f 3 f 4 prism* L1 Iris - options: FOV ~3 (4 mm) or ~ 10 (13 mm) Aperture stop ~ F / 6.5 Reflecting prism* options: 1 sun elevation 2 zenith radiance 3 horizontal irradiance 4 below: lens L1 and Hg or halogen lamp. Filter wheel #2 N.D. options: T=1 (open), T~0.3, T~0.1, T~0.03, T~0.01, T~0.003 note: ~ c/s (3.2x10 6 c/s) is the maximum useful signal. Filter wheel #1 options: GQP (diffuser) polariser opaque open 3

4 Fore-optics (2) Mode -1: no diffuser. the sun and sky are imaged on the slit. shown with the iris in the semi-closed position. no signal change when the iris is opened. sun UV image diameter ~ 1/3 of slit length. Used for: focussed sun, focussed moon and, with the polarizer, for zenith sky and umkehr measurements. Mode -2: preferred mode. GQP inserted. Used for direct-sun measurements. diffuser (GQP) in quasi-parallel light. entrance slit in a uniform patch of light coming from all directions within ~1.5 of the centre of the sun (one hopes). Advantages over mode-1: 1 tolerance of slight misalignment. 2 much reduced effects of variation in response over aperture. Disadvantages compared with mode-1: 1weaker signal. 2 larger ratio of unwanted sky signal versus wanted sun or moon signal (but smaller than for Dobson DS), which is important at low solar elevation. With diffuser: goal for FOV is 3 solar diameters == 1.5 deg. 4

5 Spectrometer layout mm The Brewer spectrometer is a modified Ebert type using one mirror. F P Exit slit #1 Entrance slit The instrument axis, defined as the normal to the front plate (FP) passing through the centre of the grating surface also passes through the vertical plate (VP) which locates the mirror. correction lens The entrance slit and exit slit#1 (not #3) are ~equidistant from the axis. The exit and exit directions of the central ray are parallel to the axis. The correction lens reduces the coma and astigmatism of the basic Ebert design. V P 5

6 Grating angles and pitch 6

7 Focusing the spectrometer right side of mirror (2) (1) left side of mirror exit slit All-2 Right-2 Lef t-2 Method: Turn on the Hg lamp, set the micrometer to give a signal for λ = nm (on slit #0 preferably) and cover all but a patch on the right side of the aperture. All-1 Scan the wavelength motor and record the step number for the peak signal, or the mean of the two half-intensity positions. Repeat for the left side of the aperture. Right-1 Move the mirror and repeat; continue with appropriate mirror movement to get it to position (2) so that the peaks at each side happen at the same steps step number. 7 Lef t-1

8 Ebert and Brewer aberrations - general The basic Ebert design results in a tilted spectrum, coma and astigmatism. Coma - the extreme rays and the axial ray do not come together - occurs with spherical mirrors used off-axis. coma Tilt of the spectrum, if not corrected, would require the exit slit mask to be rotated (by ~6 ) about a vertical axis. In the Brewer, and other modified Eberts, the tilt is minimized by moving the entrance slit back. The effective position of the entrance slit (i.e the position of its image in the correction lens) is 4.8 mm further away than the exit slits from the main mirror. Coma imposes a lower limit to the image size (see diagram). The lower limit is obtained near where the extreme rays intersect and it corresponds to a minimum width in wavelength of the transmission function- here called the aberration width (abw). The tilted correction lens in the Brewer compensates the coma in the basic Ebert. Astigmatism causes the spectral images of points on the entrance slit to be stretched out along the exit slits. Its main effect is to increase the required length of each exit slit. The cylindrical first surface of the correction lens eliminates coma at exit slit #4 and leaves small residuals (<0.45 mm) at the other slits. 8

9 Transmission function definitions Transmission function (X) - T(λ, s) is the instrument transmission where λ is the wavelength of the incident radiation and s is the wavelength setting (e.g. steps on the wavelength drive motor, or pixel number on an array detector). With F defined as the flux at the entrance slit (photons/s/m 2 ) and the direction the instrument FOV is pointing.: > dφ dθ 9

10 Transmission function definitions More complications: Transmission function (X) - TFX(λ, s) is the instrument transmission where λ is the wavelength of the incident radiation and s is the wavelength setting (e.g. steps on the wavelength drive motor, or pixel number on an array detector). Dispersion function - λ (s) is some measure of the location of T(λ,s) e.g. the value of λ where T(λ,s) is maximum or the mean value of λ weighted by T(λ,s). Transmission function -TF(λ, λ ) where λ is the wavelength identified by the dispersion function. It is usually scaled so that TF(λ, λ )=1. The aberration-limited TF is obtained with very narrow entrance and exit slits; its full width (at near-zero intensity) is the aberration width (abw). The diffraction-limited TF, which could be obtained with perfect optics and very narrow slits, is considerably narrower (FWHI ~ nm) than the aberration TF s and does not significantly affect the overall Brewer TF. 10

11 Aberration widths, Brewer It is important to keep the aberration widths (abw s) small because: (1) signal is needlessly lost if the abw is not smaller than the equivalent slit widths. (2) the abw essentially describes the extent of variation of wavelength over the aperture which causes unwanted dependency of signal on the direction of the incoming radiation. Consequently, reducing the abw makes for easier and/or more accurate calibration. The dimensions used in deriving the following information were retrieved from manufactured Brewers and are given at the end of this section. The focus used here, and recommended earlier in this section, is the intersection of the extreme rays for 296.7nm on slit #0; 326nm (Cd) on slit #5 is an alternative. The Brewer spectrum still tilts, but by only ~1.3 ( 0.40 mm between slit #0 and slit #5). At the ozone setting ( ~35.40 ), all the abw s are less than nm. They are not much degraded by errors of ± 0.2 mm in the mirror positioning screws. The abw s at the ozone wavelengths would be about half the current values if the lens tilt were reduced from 29 to 26 and if the entrance slit were moved back a further 2.3 mm. However, this improvement would not be realized over the full scanned wavelength range. 11

12 Aberration widths, Brewer v. Ebert The grating in the Brewer can be rotated over the range 32.5 o to 42 o in order to scan the UV. Corresponding wavelength ranges are ~ nm for slit #5 and ~ nm for slit #0. A consequence of the entrance slit being set back (in order to flatten the spectrum image) is that the plane of the spectrum changes when the grating is rotated, e.g. by ~2.3 mm between 300 nm and 365 nm on slit #5. This causes the abw s to increase progressively with wavelength to ~0.13 nm at the high end of the scan range. The correction lens magnifies by about 1.2 in the spectral direction and about 1.0 in the vertical. The Ebert with the same light gathering power as the Brewer therefore has an aperture 1.1 times that of the Brewer entrance, i.e. 4.2EX1.1= 4.62E angular radius. On this Ebert equivalent of the Brewer, the aberration widths (abws) at the ozone setting are in the range nm. At the high end of the scan ranges the abw s increase to ~0.23 nm (c.f.: 0.08). Astigmatism ranges from 1.5 to 2.2 mm. 12

13 Ray-traced transmission statistics : for a selection of slits and wavelength settings on the Brewer slit Wavelength exit slit width en. slit width abw grating angle deg out of focus astigmatism # nm nm nm nm mm mm

14 Slit 0 W 297 a fwhi= 636 jw= 557 Ray-traced transmission functions Starting from the bottom, the curves in each panel show: 1:aberration-limited transmission function (very narrow slits and the actual optics*) 2: the entrance slit width 3: the exit slit width 4: the overall (calculated) transmission function with the given slit widths. Abscissa- wavelength (nm) from centre Ordinate- relative transmission. Slit 1 W 325 a fwhi= 573 jw= 521 Slit a fwhi= 593 jw= Legends show, slit #, centre wavelength (nm), grating angle (degrees), entrance and exit slit equivalent widths, aberration width (abw), the full width at half intensity, and the slit width parameter from a Brewer algorithm, (last five in pm). 297 nm slit 0 - the Hg line and slit recommended for overall focusing. 310 nm - the ozone setting for slit nm on slit 1 - HeCd laser on the slit (often) used for wavelength scanning. 365 nm, the recommended long wavelength limit (necessarily on slit 5). Slit 5 W 365 a fwhi= 497 jw=

15 Post-spectrometer optics mask slits Fabry lens f = 38 mm filter Photomultiplier: detector (cathode) 10 mm diameter. White-light image of grating, ~7 mm diameter, i.e. same patch of light for all slits. Some of the more usual grating pitch options and programmable filter options Name, Mark - II III (Double) IV (Dual) V (Red) Grating pitch Filter option NiSO4+ UG 11 Nothing NiSO4 + UG11 NiSO4 + UG11 Filter option 2 -- UG 11 BG 12 (Blue Glass) OG 590/550 Filter option 3 -- choice UG 11 EPA extended scan model 15

16 Field and aperture stops [Hg & halogen lamps] [Lens1] or [UV diffuser] or SKY, SUN or MOON [Prism] [Lens 2] IRIS = FIELD STOP [Lens 3] [GQP diffuser, etc] APERTURE STOP [Lens 4] ENTRANCE SLIT GRATING EXIT SLITS PM CATHODE Explanation: Upper case objects are imaged on the following like-colored upper case object. The imaging is only very approximate with lower case objects. Thus Green corresponds MORE or less closely with the field stop, and Brown corresponds MORE or less closely with the aperture stop. The imaging of the iris stop on the entrance slit plane is absent when the GQP is in use. The imaging of the aperture stop on the grating only occurs due to the small size of the entrance slit. 16

17 Finite Counting Speed Poisson Statistics C = C 0 exp( -C 0 J ) C Observed Count Rate C 0 True Count Rate J Dead Time J ~ 40 ns So the lost counts are about 4% at 1E6 counts/s Hammamatsu tubes produce a dead time ~20 ns 17

18 Dark Count & Dead Time Correction 8350 REM correct VA for dark/dead time 8355 VA=(VA-F(1))*2/CY/IT:IF VA>1E+07 THEN VA=1E IF VA<2 THEN VA= F1=VA:FOR J=0 TO 8:VA=F1*EXP(VA*T1):NEXT 8370 RETURN 8399 : 18

19 Brewer standard direct sun measurement The Brewer measures the intensities in five wavebands when in the Direct Sun (ds) and several other routines. Using the index k to denote each of the five wavebands(2 to 6) the absorption expressions may be written as: logi k = logi 0k - (μ " k x + m β k + sec2 δ k + μ α k y ) The Brewer signals are photon counts. They are corrected for the dark signal and for non-linearity and used in place of the irradiances I k in the above and following expressions. The wavebands are roughly triangular(see later), with FWHI=0.55nm, centered on the following wavelengths (nm): k k z* dark ( * z= or 303.1, used mostly for calibration.) 19

20 Correct and Scale Counts 8300 REM generate corrected F's 8305 FOR I=WL TO WU:IF I=1 THEN VA=F(I):GOSUB F(I)=LOG(VA)/CO*P4%:J=I:IF J=0 THEN J= IF MDD$="o3" THEN X=TC(J) ELSE X=NTC(J) 8325 F(I)=F(I)+X*TE%+AF(AF%) 8330 IF C$="ds" OR C$="fz" OR C$="sc" OR C$="fm" THEN F(I)=F(I)+BE(I)*M3*PZ%/1013 :REM rayleigh 8335 NEXT:RETURN 8349 : REM ******** dt routine 12/04/95 *************** 20

21 Ozone Cross-sections GOME FM Ozone Cross-sections 273 K 241 K 202 K Spectral Resolution ~0.3 nm 21

22 Brewer DS algorithm for There are several valid ways to derive ozone values from the five measurements. The standard method does not use the measurement at 306.3nm. It is expressed in terms of weighting factors using the following notation: F k = logi k + m $ k ( F 0k = logi 0k ) WC = k w k k etc. with W = ( ) ozone The weighting factors w k are chosen so that the sulphur dioxide product WC" is zero and WC* is negligible* provided * only varies slowly with wavelength. Consequently the following equation applies: WC ( F 0 - F ) = µ x WC" This allows a solution for the ozone amount (x) for each measurement of I 1<k<6 provided WCF 0 is known, either by comparison with another Brewer on which WCF 0 is known, or by extrapolation. *W is orthogonal to the wavelength 8 k so any linear variation of * with k has minimal effect. ( c.f. Dobson double pair assumption). Brewer Workshop, Beijing, China September 12-16,

23 Ozone Calculation REM calculate ratios 8705 IF MDD$="n2" THEN FOR I=4 TO 6:MS(I)=F(5)-F(I-2):NEXT: MS(7)=F(6)-F(5):REM single ratios 8715 MS(8)=MS(4)-3.2*MS(7):REM SO2 ratio 8720 MS(9)=MS(5)-.5*MS(6)-1.7*MS(7):REM O3 ratio 8725 GOTO FOR IM=4 TO 8:MS(IM)=F(IM-2):NEXT 8735 MS(9)=.1*F(2)-.59*F(3)+.11*F(4)+1.2*F(5)-.82*F(6):REM F ratio 8740 IF PO%=1 THEN PRINT#4,SPC(30); 8745 FOR I=4 TO 9:MS(I)=INT(MS(I)+.5) 8750 IF PO%=1 THEN PRINT#4,USING "########";MS(I); 8755 NEXT:IF PO%=1 THEN PRINT#4, 8760 MS(1)=T0:MS(2)=ZA:MS(3)=M2: IF MDD$="o3" THEN MS(12)=F(2):MS(13)=F(6) 8790 RETURN 23

24 Ozone Calculation REM calculate ozone 8805 IF C$="sl" OR C$="um" OR C$="up" THEN RETURN 8810 IF C$="zb" OR C$="zc" OR C$="zp" OR C$="zs" THEN MS(11)=(MS(9)-B1)/A1/M2:REM direct data 8820 MS(10)=((MS(8)-B2)/A3/M2-MS(11))/A GOTO A=ZSC(1)+ZSC(2)*M2+ZSC(3)*M2*M2-(MS(9)-B1)/P4%: REM zenith data 8835 B=ZSC(4)+ZSC(5)*M2+ZSC(6)*M2*M C=ZSC(7)+ZSC(8)*M2+ZSC(9)*M2*M A=B*B-4*A*C:IF A<0 THEN A= MS(11)=(-B+SQR(A))/2/C*P4% 8855 MS(10)=((MS(8)-B2)/A3/M2-MS(11))/A MS(10)=INT(MS(10)+.5)/10:MS(11)=INT(MS(11)+.5)/ PRINT#4,USING SPACE$(19)+"O3 =####.# SO2 =####.#"; MS(11);MS(10) 8870 RETURN 24

25 Ask me about the South Pole Brewer Workshop, Beijing, China Thank you for your attention September 12-16,