Comments on: Grating Dispersion [Equation of the Week] http://hea-www.harvard.edu/AstroStat/slog/2008/eotw-grating-dispersion/ Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 01 Jun 2012 18:47:52 +0000 hourly 1 http://wordpress.org/?v=3.4 By: vlk http://hea-www.harvard.edu/AstroStat/slog/2008/eotw-grating-dispersion/comment-page-1/#comment-274 vlk Tue, 08 Jul 2008 03:51:50 +0000 http://hea-www.harvard.edu/AstroStat/slog/?p=315#comment-274 As written, the expression for the fractional error in wavelength is a direct consequence of propagating the statistical error via the <s>method of moments</s> delta method and does assume a Gaussian error model. Given the location of the photon on the detector, it is clearly not possible to assign a wavelength to it to an accuracy better than the PSF. The uncertainty in the grating period is usually determined by the tolerances in the construction, which are usually quite stringent and far better than the PSF size, and so are quite negligible. The line spread function (LSF) therefore is almost entirely determined by the PSF. This is not the systematic error. Any systematic errors that are present are in addition to these errors. As written, the expression for the fractional error in wavelength is a direct consequence of propagating the statistical error via the method of moments delta method and does assume a Gaussian error model.

Given the location of the photon on the detector, it is clearly not possible to assign a wavelength to it to an accuracy better than the PSF. The uncertainty in the grating period is usually determined by the tolerances in the construction, which are usually quite stringent and far better than the PSF size, and so are quite negligible. The line spread function (LSF) therefore is almost entirely determined by the PSF. This is not the systematic error. Any systematic errors that are present are in addition to these errors.

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By: hlee http://hea-www.harvard.edu/AstroStat/slog/2008/eotw-grating-dispersion/comment-page-1/#comment-273 hlee Mon, 07 Jul 2008 21:53:18 +0000 http://hea-www.harvard.edu/AstroStat/slog/?p=315#comment-273 Irrelevant question but an extension from <a href="http://hea-www.harvard.edu/AstroStat/slog/2008/q-systematic-error/" rel="nofollow">[Q]systematic error</a>: From <i>"The nominal statistical uncertainty on the estimated wavelength can be written as a combination of the measurement uncertainties in the grating periodicity d and the uncertainty in the photon’s position wrt the 0th-order ..."</i> since statistical uncertainty accompanies probability distribution (given or subject to be estimated, parametric or nonparametric), I wonder if this statement is implying that wavelength has a (parametric) distribution whose parameters are associated with <i><u>the measurement uncertainties</u> in the grating periodicity</i> and <i><u>the uncertainty</u> in the photon’s position</i>? Do people estimate this distribution in terms of these parameters? Is <i><u>the nominal statistical uncertainty</u></i> a joint distribution of these two parameters? or <u>plainly assume Gaussian and additive errors</u>? I'm still seeking answers to <b>systematic errors</b>, measurement errors, and how to model these uncertainties. Thanks~ p.s. I think I'll understand this post better if I scrutinize later. A first time reading hardly provided me anything. p.p.s. I came back to read again but another thought came to me. I do not recall that I saw <u>Kalman filter</u> or <u>HMM</u> occasionally from astro-ph but I imagine that the things I learned from <u>nonlinear control and system</u> could help modeling some of astronomical systems with systematic errors or measurement errors in addition to known statistical errors. (Here, known means not quantification but qualification; for example, not estimated &#963 but Poisson noise). As astrometry is a subject in astronomy, I hope handling errors to be regularized. I'll appreciate any criticism and comments to my question. Irrelevant question but an extension from [Q]systematic error:
From “The nominal statistical uncertainty on the estimated wavelength can be written as a combination of the measurement uncertainties in the grating periodicity d and the uncertainty in the photon’s position wrt the 0th-order …”
since statistical uncertainty accompanies probability distribution (given or subject to be estimated, parametric or nonparametric), I wonder if this statement is implying that wavelength has a (parametric) distribution whose parameters are associated with the measurement uncertainties in the grating periodicity and the uncertainty in the photon’s position? Do people estimate this distribution in terms of these parameters? Is the nominal statistical uncertainty a joint distribution of these two parameters? or plainly assume Gaussian and additive errors? I’m still seeking answers to systematic errors, measurement errors, and how to model these uncertainties. Thanks~

p.s. I think I’ll understand this post better if I scrutinize later. A first time reading hardly provided me anything.

p.p.s. I came back to read again but another thought came to me. I do not recall that I saw Kalman filter or HMM occasionally from astro-ph but I imagine that the things I learned from nonlinear control and system could help modeling some of astronomical systems with systematic errors or measurement errors in addition to known statistical errors. (Here, known means not quantification but qualification; for example, not estimated σ but Poisson noise). As astrometry is a subject in astronomy, I hope handling errors to be regularized. I’ll appreciate any criticism and comments to my question.

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