Dispersion issues for Holospec spectrometers at JET. T.M. Biewer, Oak Ridge National Lab. August 18th, 2008, Culham Science Center

Size: px

Start display at page:

Download "Dispersion issues for Holospec spectrometers at JET. T.M. Biewer, Oak Ridge National Lab. August 18th, 2008, Culham Science Center"

Terence Jennings
5 years ago
Views:

1 Dispersion issues for Holospec spectrometers at JET T.M. Biewer, Oak Ridge National Lab. August 18th, 2008, Culham Science Center T.M. Biewer 1 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

2 Motivation Kaiser Optical Holospec spectrometers at JET KS5D, KS5E, KS7D, KS7C,... Short focal-length leads to non-constant dispersion across the image plane (CCD camera) Difficulties in determining the dispersion Difficulties in analysis within CXSFIT Inconsistency between KS5C (Czerny-Turner system) and KS5D measured C VI T i and v T T.M. Biewer 2 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

3 Outline The grating equation for Holospec instruments Validity of 2 nd order polynomial approximation, in principle Fitting of Sm lamp calibration data to derive the wavelength calibration and dispersion Issues with pulse data: Be, C positions Discussion T.M. Biewer 3 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

4 Theory T.M. Biewer 4 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

Short focal length spectrometers Design pioneered by R.E. Bell at PPPL Multiple curved entrance slits 20 channels/instrument Spectrometer Kaiser Optical Holospec f/1.

5 Short focal length spectrometers Design pioneered by R.E. Bell at PPPL Multiple curved entrance slits 20 channels/instrument Spectrometer Kaiser Optical Holospec f/1.8 Transmission gratings for high throughput CCD camera Roper Cascade 512B Roper PhotonMax 512 Fast framing (5 or 10 ms) Rotary chopper Scitech Instruments 300 Prevents image smearing during read-out T.M. Biewer 5 (13) PC driven Core Spec Grp Mtg, JET, UK 18 Aug. 2008

λ = λ 0 cos γ[sin(θ 1 +φ 1 ) + sin(θ 2 +φ 2 )]/ [sin θ 1 + sin θ 2 ] λ= λ 0 cos γ[sin(θ 1 +φ 1 ) + sin(θ 2 + tan -1 (x 2 /f 2 ))]/ [sin θ 1 + sin θ 2 ] λ= A t [B t + sin(c + tan

6 Holospec Grating Equation Grating Equation: λν = cos γ[sin(θ 1 +φ 1 ) + sin(θ 2 +φ 2 )] ν =[sin θ 1 + sin θ 2 ]/λ 0 tan φ 1 =x 1 /f 1 tan φ 2 =x 2 /f 2 tan γ=y 1 /f 1 =y 2 /f 2 (x 2,y 2 ) are coordinates on the CCD. For a given track y 2 is constant. λ 0 is the center wavelength of grating. λ = λ 0 cos γ[sin(θ 1 +φ 1 ) + sin(θ 2 +φ 2 )]/ [sin θ 1 + sin θ 2 ] λ= λ 0 cos γ[sin(θ 1 +φ 1 ) + sin(θ 2 + tan -1 (x 2 /f 2 ))]/ [sin θ 1 + sin θ 2 ] λ= A t [B t + sin(c + tan -1 (x 2 /D))] λ/ x 2 = (λ 0 /f 2 ) cos γ cos(θ 2 + tan -1 (x 2 /f 2 )) cos 2 (tan -1 (x 2 /f 2 ))/ [sin θ 1 + sin θ 2 ] λ/ x 2 = (A t /D) cos(c + tan -1 (x 2 /D)) cos 2 (tan -1 (x 2 /D)) T.M. Biewer 6 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

7 Holospec grating equation (cont.) λ= A t [B t + sin(c + tan -1 (x 2 /D))] λ/ x 2 = (A t /D) cos(c + tan -1 (x 2 /D)) cos 2 (tan -1 (x 2 /D)) A t = λ 0 cos γ /[sin θ 1 + sin θ 2 ] B t = sin(θ 1 +φ 1 ) C= θ 2 D= f 2 = (5290 Å) cos γ /[sin40 +sin50 ] ~ /- 5 Å = sin(40 + φ 1 ) ~ / = 50 = 58 mm nominal values for KS5D curved entrance slits T.M. Biewer 7 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

8 Binning into tracks The CCD is vertically binned into tracks, corresponding to fibers viewing different radial NBI volumes. Curved entrance slits ensure that spectral lines have minimal deviation (horizontally) within a track. T.M. Biewer 8 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

9 Simulated KS5D dispersion v = c λ s /λ 0 = c p s d/ λ 0 Δv = v a -v m = c(d a -d m )p s / λ 0 Δv/v = (v a -v m )/v = (d a -d m )/d =Δd/d To first order in dispersion differences. Calculated λ(p) and d(p) binned over actual KS5D track definitions. 2 nd order polynomial fit to λ(p) over the range of KS5D filter bandpass. Δv/v=Δd/d<0.1% It is valid for CXSFIT to linearly approximate d(p) within passband. T.M. Biewer 9 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

10 Calibration sensitivity Sensitivity to Dispersion: Sensitivity to wavelength offset : v = c λ s /λ 0 = c p s d/ λ 0 Δv = v a -v m = c(d a -d m )p s / λ 0 Δv/v = (v a -v m )/v = (d a -d m )/d =Δd/d 1% error in dispersion implies 1% error in measured velocity. v = c λ s /λ 0 = c (λ-λ 0 )/ λ 0 Δv = v a -v m = c[(λ a -λ 0 )- (λ m -λ 0 )]/ λ 0 =c (λ a -λ m ) / λ 0 Δv/v = (v a -v m )/v = (λ a -λ m ) / (λ m -λ 0 ) = [(ε a +λ s +λ 0 )- (ε m +λ s +λ 0 )] /[ (ε m +λ s +λ 0 ) -λ 0 ] = (ε a - ε m ) /(ε m +λ s ) = ε m /(ε m +λ s ) Δv/v =[ε m /λ 0 ]/[v/c+ ε m /λ 0 ] If v T ~300 km/s then v/c~0.001, 1% error in wavelength offset implies ~100% error in measured velocity 0.1% error in wavelength offset implies ~50% error in measured velocity. 0.01% error in wavelength offset implies ~10% error in measured velocity. T.M. Biewer 10 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

11 Sm calibration data ~1% error in dispersion ~1% error in meas. velocity ~0.2 to 0.5 Å offset error ~0.01% error in λ offset ~10% error in meas. velocity Finding line centers to this accuracy implies ~1/4 pixel resolution for KS5D T.M. Biewer 11 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

12 Pulse data (73916) Applying calibration from Sm lamp to JET data shows substantial offsets Non-stationary passive, edge lines? Limit to instrument resolution? Poor calibration? Correctible within CXSFIT T.M. Biewer 12 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

13 Discussion How should dispersion for these instruments be determined? Fit to Sm calibration data (good enough?) incorporate pulse data, C, Be, etc.? Use first principles function or 2 nd -order polynomial? T.M. Biewer 13 (13) Core Spec Grp Mtg, JET, UK 18 Aug. 2008

In situ wavelength calibration of the edge CXS spectrometers on JET

EUROFUSION WPJET1-PR(16) 15408 E Delabie et al. In situ wavelength calibration of the edge CXS spectrometers on JET Preprint of Paper to be submitted for publication in 21st Topical Conference on High