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Q: Mapping Table from IR Wavelength to Temperature of source ( Answered,   3 Comments )
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 Subject: Mapping Table from IR Wavelength to Temperature of source Category: Science Asked by: dadadee-ga List Price: \$50.00 Posted: 23 May 2003 08:57 PDT Expires: 22 Jun 2003 08:57 PDT Question ID: 207741
 ```Hi, I'm looking for a table of values mapping the wavelengths of Infra-red radiation emission to specific temperature values (of a given source) between 35.0 to 40.0 degrees celsius (0.1 deg celsius resolution). My search has yielded an approximate value of 10 microns for temperatures in this range but I require the specific mappings. An example of how the table might look like: IR Wavelength (microns) Temperature ----------------------- ----------- 8.0 35.0 8.1 35.1 8.2 35.2 These are fake figures. I will also need to know if there are manufacturers which produce IR filters of the various IR wavelengths (to cut out radiation corresponding to certain temperatures) listed in the table. Thanks. Best wishes, Leon``` Request for Question Clarification by mathtalk-ga on 24 May 2003 21:04 PDT ```Hi, dadadee-ga: Racecar-ga has correctly sketched out for you the existence of a spectral "peak" in the black-body radiation curve which depends on absolute temperature. Such a peak is rounded, rather than sharp, however, which adds to my confusion about what you require in connection with manufacturers of filters "to cut out radiation corresponding to certain temperatures". Can you point out an example of the sort of filter you have in mind? regards, mathtalk-ga```
 Subject: Re: Mapping Table from IR Wavelength to Temperature of source Answered By: welte-ga on 25 May 2003 14:18 PDT
 ```Hi racecar-ga, Thanks for your question. The general formula for the peak wavelength of blackbody radiation emitted by a warm body is as follows: Lambda [microns] = 2900 / T [deg K], where Lambda is the wavelength of the light in microns, and T is the temperature in Kelvin. To convert from Kelvin to Celcius, Kelvin = Celsius + 273.15, so the equation becomes Lambda[microns] = 2900 / (T [celsius] + 273.15). I generated an Excel spreadsheet to chug through the numbers and create the following table: Temperature Peak Wavelength (Celsius) (Microns) ---------------------------- 30.0 9.56622 30.1 9.56307 30.2 9.55991 30.3 9.55676 30.4 9.55362 30.5 9.55047 30.6 9.54733 30.7 9.54418 30.8 9.54104 30.9 9.53790 31.0 9.53477 31.1 9.53164 31.2 9.52850 31.3 9.52537 31.4 9.52225 31.5 9.51912 31.6 9.51600 31.7 9.51288 31.8 9.50976 31.9 9.50664 32.0 9.50352 32.1 9.50041 32.2 9.49730 32.3 9.49419 32.4 9.49108 32.5 9.48798 32.6 9.48487 32.7 9.48177 32.8 9.47867 32.9 9.47558 33.0 9.47248 33.1 9.46939 33.2 9.46630 33.3 9.46321 33.4 9.46012 33.5 9.45704 33.6 9.45395 33.7 9.45087 33.8 9.44779 33.9 9.44472 34.0 9.44164 34.1 9.43857 34.2 9.43550 34.3 9.43243 34.4 9.42936 34.5 9.42630 34.6 9.42323 34.7 9.42017 34.8 9.41711 34.9 9.41406 35.0 9.41100 35.1 9.40795 35.2 9.40490 35.3 9.40185 35.4 9.39880 35.5 9.39576 35.6 9.39271 35.7 9.38967 35.8 9.38663 35.9 9.38359 36.0 9.38056 36.1 9.37753 36.2 9.37449 36.3 9.37147 36.4 9.36844 36.5 9.36541 36.6 9.36239 36.7 9.35937 36.8 9.35635 36.9 9.35333 37.0 9.35031 37.1 9.34730 37.2 9.34429 37.3 9.34128 37.4 9.33827 37.5 9.33526 37.6 9.33226 37.7 9.32926 37.8 9.32626 37.9 9.32326 38.0 9.32026 38.1 9.31727 38.2 9.31428 38.3 9.31129 38.4 9.30830 38.5 9.30531 38.6 9.30233 38.7 9.29934 38.8 9.29636 38.9 9.29338 39.0 9.29041 39.1 9.28743 39.2 9.28446 39.3 9.28149 39.4 9.27852 39.5 9.27555 39.6 9.27258 39.7 9.26962 39.8 9.26666 39.9 9.26370 40.0 9.26074 There are several ways to go about filtering out these wavelengths, depending on your specific application and how narrow a band around the peak you will need to filter. Without details of your project, I will only be able to make some general suggestions in this regard. Feel free to ask for clarification. If you're looking a static (non-changing) object, then possibly the most cost-effective method of putting such a project together (if you're thinking of small quantities) would be to use so-called "wedge filters." These filters have a different peak transmission at different positions along the filter (i.e., at one end, they may only pass 9.0 microns, at the other end, they may only pass 9.5 microns). You could position a single filter in the path of the incoming light and simply vary the position (e.g. using a stepping motor) to change the center of the filtration. The variation in the peak is linear along the position of the filter, making the use of a stepping motor much easier. After looking at several companies, the best bet for such a filter at these wavelengths seems to be Barr Associates. They're both in the US and UK. Here's a link to their wedge filter page (UK): http://www.barr-associates-uk.com/IR%20Page.htm Barr Associates can make a narrow band pass filter to your specifications. They've worked in the astronomy / astrophysics arena, so they can make fairly narrow and complicated spectra band filters. They have some of their IR filter profiles online at this site: http://www.barr-associates-uk.com/IR%20Page.htm The animated figure on the above page demonstrates the principle of the IR wedge filter. The figure only goes out to 7microns, however Barr Associates is one of the few companies that goes to longer wavelengths in filter design. They state that they can design filters out to 35 microns. You would need to move the filter across the light path, buiding up an image (e.g. on a CCD camera or film) then block the light path while the filter moves through the range of wavelengths you don't want, then uncover the aperature as the filter moves to wavelengths you want to keep. This may be too slow or complicated to implement, depending on your project. The US home page of Barr Associates is here: http://www.barrassociates.com/ Another simpler, but more expensive, option would be to buy notch filters (filters that pass all wavelengths except a narrow band). These could be placed in the light path and would filter out the unwanted wavelengths without moving anything. This solution may work better for more dynamic objects, where you can't take the time to move a wedge filter across the entire light aperature. Barr Associates also makes custom notch filters. They also make filter arrays, so you could mount many filters on a wheel and spin it to the needed position. Finally, Barr can make custom Edge filters, which have transmission spectra that look like a step-function (on for a range of wavelengths, off for wavelengths above or below a cutoff). Here's a link for those: http://www.barrassociates.com/opticalfilters.php?type=edge Transmission spectra for samples of all these types of filters are available by clicking on one of the filter selections on each given page in the lower right corner. Another possible supplier is NDC Infrared, although they state that their narrow band pass filter upper limit is 5000 nanometers (5 microns). http://www.ndcinfrared.com/products/newtfod/narrow/narrow.html If your project is of an academic nature, you may be able to collaborate with an academic lab. One such lab is the Infrared Multilayer Lab at University of Reading (UK), Department of Cybernetics. Here's a link to their filter page: http://www.cyber.rdg.ac.uk/ISP/infrared/products/coatings.htm and a link to an example of their custom notch filter work: http://www.cyber.rdg.ac.uk/ISP/infrared/products/notch.htm References: A good dicsussion of blackbody radiation can be found at: http://www.cosmicshell.com/~miranda/lab/BBradiation/BBradiation.html I hope this was helpful. Please feel free to request clarification or provide more details on your project if you require other filter suggestions. Also, let me know if you require more digits in the peak wavelength table above, or a wider range of temperatures. -welte-ga```
 ```A warm body emits a wide range of wavelengths. If you're interested in the wavelength at which power peaks, I think you need to specify whether power per unit frequency (wavenumber) or power per unit wavelength. I think they don't peak at the same place. In any case, the Planck radiation law will tell you all you want to know. I plugged 30 C and 40 C in and got that the power per unit wavelength peaks at 9.57 microns and 9.27 microns respectively (note that higher temperature correspond to shorter wavelengths, unlike in your table).```
 ```Thanks for the information. As mentioned, I would need the complete table for wavelength against temperatures in the range of 35 degrees celsius to 40 degrees celsius at 0.1 degree intervals. I would also need a list of manufacturers who are able to produce the IR filters for the corresponding temperatures before I can accept the submission as an answer. Thank you once more. PS: Please feel free to clarify any doubts that you may have. Leon```
 ```Wow, \$50 for this? At least he should have gotten it in generic form: peak wavelength = 0.000293 m/Temperature (in Kelvin)```