JRWASTRO

Not to worry, as we say. I only wish to point out that the filtering algorithm should calculation of the polynomial coefficients at each step. In the example I used if you use a polynomial of order 11 and padded the data file with 5 points on the front and back one will need to compute 2000 polynomial sets. About the DFT - it is evaluated using the Fast Fourier Transform - but that is another issue!! The FT of a signal is complex - it has a magnitude and a phase. For real signals the FT will exhibit Hermitian Symmetry (a very important property). When you multiply the X(f) by its complex conjugate X*(f) you will get a real value representing a power spectrum etc. etc. etc. FYI I can take two signals x1(t) => X1(f) and x2(t) => X2(f) and obtain : S12(f) = X1(f) x X2*(f) which is the cross power spectral density and is a complex function which tells us about the correlation between the two functions - especially the phase of the PSD. Jeremy.

Very good. Please tell me how many polynomial coefficient sets do I need to use here: My noisy data set has c. 22000 points of a complex waveform. The data is, of necessity, complex it is at 0Hz. LPF here produces a BPF. Jeremy.

Nothing strange about this. Interesting comparison though. Re: We can do much better than that. The author talks about a 16 moving average but does not tell us about the length of the impulse response of the LPF. Perhaps he/she needs to show the response of different length LPF's.

Greetings Steve, Implement the SG filter and presenting the results will need some software like MATLAB (very expensive) or OCTAVE (free open source software). Create a list of your raw data (CSV) that can be read by OCTAVE and it will be straight forward to implement a SG filter and or a Moving Average (MA) filter. For the SG filter you will need to calculate the polynomial coefficients at each point. Calculation of the coefficients involve some matrix manipulations like multiplications and inverse of a matrix. Octave is suited ideally to do these calculations. Once you have obtained these polynomial coefficients a filtering algorithm may we written. This algorithm may be used to do a MA filter (set all the coefficients = 1.0) or the SG filter. The SG filter is a general version of a MA filter and will be superior in preserving peaks. Plotting / presentation of the results is presented easily using OCTAVE. -- OCTAVE 6.2.0, c.2021, is available for download. Jeremy.

Greetings Steve, Re: Is that a daft idea? Definitely not ! What you are doing is a moving average. This is equivalent to low pass filtering where the noise bandwidth is determined by the bandwidth of this LPF. The more you "stack" the lower will be the bandwidth. But remember too much averaging will "smear" the results you will be looking for. You are trying to obtain a graph of the brightness vs time so the sampling rate must be at least twice the highest rate of the brightness change - please see Nyquists sampling theorem. You need to take into account the period of the changing brightness. ie. the sampling frequency is 1/40 Hz. If the change in brightness is very slow compared to 400s (ie. 10 x( 30s + 10s) ) then you are good to go!! ie take 30s samples and average 10 at a time as you have said. Your last strategy would be the way to go. Jeremy.

Greetings Robin, Regarding the first link : One will always find someone who has done all the hard work ! Now I'm getting somewhere. The first link is exactly what is needed. Those equations are easy to code in Octave. Why, even with my schoolboy French I can read the paper (in parts). As an aside, L'absorption par la molécule d'ozone reminds me of my youth where I was given the task of measuring the amount of pricipitable water vapor in the atmosphere, in a given range, for our thermal (8 to 14 micro metres) imagers. But that was many years ago. Regarding the second link: I will have to struggle through this one but the conclusion is encouraging ie. quote On a démontré ici la possibilité de mesurer la transmission atmosphérique absolue avec un équipement simple et un peu de méthode unquote Thank you indeed, Jeremy.

Greetings Robin, Thank you for your response. Re: If you are only interested specifically in the sky brightness in each photometric band though why not measure it directly from images taken through each filter using stars as flux references? Yes exactly that is what I will be doing measurement in the Johnson R,V,and B bands in a hemispherical dome. Re: (Though you would still need to correct the stellar fluxes for the effects of atmospheric extinction) Yes. This is where I will have to find a suitable model. Re: The spectrum of a star varies significantly in both intensity and the shape of the spectrum with altitude depending on the air mass, due to atmospheric extinction. I did not even think about it until now. But I will heed to incorporate a model as I will be taking data in a dome (0 to 360 degrees (azi) and 0 to 90 degrees. elevation) . I have a feeling that this might not be straightforward as one will need environmental data. Initially I am taking data and I am improving my methodology to taking a single "hemisphere worth" of data. When I get this down to a fine art I will take the data in 3 bands (R, V and B). In the mean time I am exploring spectroscopy - to this end I will be getting the Star Analyser 200 - excellent stuff!! Thank you for your time, Kind Regards, Jeremy.

For the purpose of photometry one would be looking to improve the output SNR. Your best estimate of the signal in the noise will be the expected value of the signal (please see expected value / statistical expectation) this will be the average value i.e. sum/total. This works because the average value of the noise is zero. The improvement in SNR is sqrt(number of samples averaged) in this case one may expect an improvement of 1.7321. Perhaps you may try 4 exposures of 15s for a 2:1 improvement in SNR.

Re: I am not clear what you want to measure the spectra of ... I am interested in measuring the spectrum of the background (only) at various altitudes. What I would like to measure is sky background brightness (power per unit solid angle per unit area or watts per steradian per square metre projected area) ) I would like to get an estimate for each band, To that end I need to take measurements at various azimuths and altitudes. Re: how a stars spectra changes with altitude ... I do not think that this will happen (?) but I would take spectra of the stars above 30 degrees elevation. The star spectra on average will be different than the background and will be used as a discriminator to select the background only. This is one of the resources I use: https://voservices.net/filter/ Thank you for the link - Just had a cursory look and it looks excellent. Need to spend much more time looking at the content and that I will do ! In a previous post you asked about my telescopes. For star measurements I use a Takahashi Mewlon 250CR and for wider FoV measurements a (well corrected) Sigma Lens (8 to 14mm). Thank you, Andrew, for taking the time to reply, Jeremy.

Here are 3 pictures, of our southern skies at Sandy Creek, taken the other night. I need to look at the spectra between the horizon and at zenith. What I am looking for is a spectrum analyser with about 10 bands in the visual each band about 35nm( (750-400)/10) wide . I imagine this resolution will will help to determine a characteristic signature. I will be taking photometric measurements in the John-Cousins R, V, and B bands. Jeremy

Thank you Andrew. That's a start for me. What I would like to do is obtain the spectrum of the light of a star and/or the light of diffuse source (scattered light) and record this spectrum (amplitude vs. wavelength) for analysis etc. Jeremy.

Greetings Readers, I have no experience in the field of stellar spectrometry however I am undertaking some research that necessitates the measurement of the spectra of various light sources, stars etc. Please tell me about commonly used spectrometers in the field of amateur astronomy their availability and cost. My budget is modest so professional level instruments are out of the question. Many thanks in advance, Jeremy.

Good attempt ET. 1. Focus needs to be better. 2. For a better result with the 50mm lens you can open the shutter for 20s with no noticeable star trails. For this exercise just stack 4 frames - "plenty good enough". 3. I have taken a picture of the cross with a single 15s exposure that shows much detail. Jeremy.

Very sad but this is what one is driven to use : 1. https://optcorp.com/products/zwo-duo-band-filter-2 and a bit more expensive 2. https://optcorp.com/products/radian-telescopes-2-inch-triad-ultra-filter Sad. Jeremy.

Greetings Roy, Re: Increasing light pollution is the bane of all astronomers Yes light pollution (LP) is the bane of all astronomers and as I have discovered there is absolutely nothing that can be done about this. Notice that with all the talk of action to reduce LP it is actually increasing. So instead of complaining about LP I have decided to study it and write a paper about it. Will this be of use? Of course not. But it will a nice paper. If I was young enough I could make a career out of this LP study. Why ? I could convince a moneyed sponsor that my work could save them a great deal of money. As Sir Humphrey Appleby would say "I am a moral vacuum". Jeremy.

Re: I believe it's usually more common in 4WD cars etc Yes! But you will have to pay. Cheap Chinese rubbish, in most cases, will not fit the bill!! The unit above looks excellent. Jeremy.

Greetings Billy, You have raised many questions that only a course in physics will help answer. I could offer a few buzz words to aid in your research. 1. Re: thermal energy and black body radiation. Thermal radiation is exactly that - radiation one can feel as heat, from a bar radiator for example. This energy will be in the vicinity of 8 to 14 micrometers (human body temperatures) and 3 to 5 micrometers in the case of Jet engine exhausts. Buzz words : See Stephan-Boltzmann law and look up Ultra violet catastrophe - See Wein's displacement law. 2. A Black Body can and will emit "Thermal Radiation" depending on its temperature. BTW. Black bodies are not black as such they can be dull red (hot) or white hot or extremely cold (above absolute zero). 3. About Buzzword : Look up Entropy and the work of Ludwig Boltzmann 4. You should study about the dual nature of radiation - waves and particles. The waves will be electro-magnetic waves - orthogonal electric and magnetic fields - look up "Poynting Vector" Good luck in your research, Jeremy

Hiya Msacco, Here is a very robust unit : https://www.redarc.com.au/smart-start-bcdc This will suite your 75Ah deep cycle battery. Jeremy

Re: send commands to my mount via Matlab without passing trough a Synscan controller but I'm not sure if it is do-able. Brave man! You can do anything with MATLAB and Simulink ( https://au.mathworks.com/products/simulink.html ) How much cash have you got ? These mathworks chaps charge like a "wounded bull" ! Have you seen the open source approximation to MATLAB called OCTAVE ? Jeremy.

I have a 10" dob like the one you have and place a 20 Ah battery as close to the centre as is possible. The OTA just misses the battery. As they say " a miss is as good as a mile". This arrangement works well but I am looking for a "cheap" lithium battery of 20Ah but, so far, I have been unsuccessful. Hope this helps. Jeremy.

Greetings Brodie, Re: B " In space, the angular resolution of the Keck telescope is govererned by the diffraction limit. " Really ? Where did you read this ? About diffraction limited optics, These books have definitions of what it means when an optic is diffraction limited: 1. Introduction to Fourier Optics by Joseph W. Goodman See p. 129 " An imaging system is said to be diffraction limited if ..... " 2. Aberration Theory Made Simple. (SPIE PRESS Tutorial Text) by Virendra N. Mahajan See p. 79 " The aberration-free image of an object is also called its diffraction-limited image .... " 3. Basic Optics for the Astronomical Sciences (SPIE PRESS) James B. Breckinridge P. 227 10.2.2 High-angular-resolution astronomy: stelar diameters. BTW : Nice picture of the Keck Telescopes on the front cover. 4. Diffraction, Fourier Optics and Imaging Oran K. Ersoy p.142 " An optical system is diffraction limited if ... " Ersoy, here, refers to Goodman (ref # 1 above). I have other books but the above references will help you answer your question. Jeremy

nil desperandum . This is the cure all in two parts :- 1. According to Douglas Adams, I quote " 85% of all known worlds in the Galaxy, be they primitive or highly advanced, have invented a drink called jynnan tonnyx, or gee-N'N-T'N-ix, or jinond-o-nicks, or any one of a thousand or more variations on the same phonetic theme. The drinks themselves are not the same, and vary between the Sivolvian 'chinanto/mnigs' which is ordinary water served at slightly above room temperature, and the Gagrakackan 'tzjin-anthony-ks' which kill cows at a hundred paces " 2. https://www.craftginclub.co.uk/join-freeginspecial?om_campaign=omme_de8a9efc-b34_1816_3101&om_send=72c0b67ce098420495697aefbc72fcf8&utm_campaign=omme_de8a9efc-b34_non_members_free_gin_170519&utm_content=freegin170519&utm_medium=email&utm_source=ometria Jeremy.

Two points:- Point 1. OK with equation 78 when A and B are the sides of a right angle triangle. B is the hypotenuse. If A/B --> 0 then the angle theta tends to 90 degrees. Cos(90) = 0 and Sin(90) = 1 (angle in degrees) Seems to be a mix-up here, perhaps what was meant:- Lim ((sin(a)) ) / a --> 1 a --> 0 It is written like this because as the angle a=0, sin(a) = 0 and the division 0/0 is meaningless. When the angle is tends to 0 radians then a = sin(a). If A/B = sin(a) when a --> 0 then we can say the angle a in radians is a = A/B Point 2. One does not need to go through the above reasoning if one uses the definition that on a circle (radius r) the length of the arc (S) is S = r * a where a is the subtended angle at the centre of the circle. For very small angles the arc and chord may be taken to be of the same length. Distance to the star may be calculated from: r = S/a. Angle a may be measured by the large land based telescopes. I see no problems here. Re: You can measure the position of the star ie the centroid of the star image to much greater precision than the resolution. Yes of course. Good point. Jeremy

Greetings Observers, Here is a link telling us about Jupiter being in opposition. It will be very bright and large : https://in-the-sky.org/news.php?id=20190610_12_100 Hope the weather is excellent on the 10-June-19. Jeremy.