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Computational Assessment of Filter Stacks

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#1 Andy Perrin

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Posted 03 November 2017 - 05:36

Computational Assessment of Filter Stacks

Abstract

Two important attributes for a filter or stack are (1) how much UV light is transmitted, and (2) how well the filter(s) prevent visible and IR contamination. Figures of merit to describe these attributes were developed and then calculated based on online spectroscopic data from Schott and other manufacturers. Mean transmittance in the UV was chosen for the first attribute, and Safety, defined as the log of the ratio of how much UV is transmitted to how much visible and IR is transmitted, was chosen for a measure of IR blocking ability. Then the results are plotted against each other to give some idea of how the stacks behave in comparison to each other. The conclusion seems to be that S8612 and UG11 produced the best stacks of those computed. The actual behavior of a filter will depend also on the camera sensor, so it is impossible to declare an absolute winner.

Definitions

I decided that "UV" meant 310nm to 400nm, and the rest of the spectrum went from 400nm to 1100nm where silicon sensor cameras stop recording. Provided one has high quality data for transmittance across the whole range from 310nm to 1100nm, then it is possible to compute some figures of merit for these attributes. And there's the rub. For most proprietary filters, including the Baader, one can only find rough numbers for the transmittances, usually in the form of linear-scaled graphs which essentially hide any IR leaks. Even when numbers are available, often they don't cover the whole range. Therefore the following discussion will be limited to situations where one can compute the values, and even then, published spectra can be inaccurate, especially for the non-Schott glasses (allegedly).

The two metrics chosen were mean transmittance in the UV, and “Safety”, defined here as the log of the ratio of area under the UV to the area under the rest of the transmittance curve. More Safety means one is less likely to have one’s image contaminated with IR or visible, for a given exposure and camera setup.

A stack that transmits only UV light and has perfect blocking of IR and visible would have infinite Safety, while one that transmits equal amounts of IR and UV would have Safety=0 by this definition, and one that transmits more visible and IR than UV would have negative Safety.

Example and Results

The exact calculation is shown in this example figure. Note that although I have plotted the curves on a diabatic graph, the calculation is done with the original transmittances, not their logs or any transformed version.

Attached Image: example.jpg

One can then plot all the stacks on a chart based on the two attributes. The boundary of the pink areas define the median values of the stacks based on each attribute. The median Safety was 3.42, and the median of the average transmittances was 0.27. The best stacks, in the sense of being the best compromise, are in the white area, and the worst are in the dark pink area. The "winner" seems to be something like 1.75mm S8612/ 1mm UG11 of the stacks examined, but clearly other considerations may alter that conclusion. The sensitivity of the camera has not been included in this calculation, so if (for example) one owns a camera with a sensor that is highly IR sensitive relative to UV, then selecting a filter with a higher Safety might lead to better photos in principle. Likewise, a camera with better UV sensitivity would benefit from less Safety and higher mean transmittance.

Attached Image: Filter Selection Chart.jpg

Finally, here are the actual spectra, again on a diabatic plot so that the IR leaks can be seen.

Attached Image: Filter spectra (companion to selection chart).jpg

Technical Details

Now to the details of how the transmittances are calculated.

Curves were fitted using cubic splines to the published spectra of each glass, after converting the raw numbers into absorption coefficient form (absorption coefficient is the fraction of the light removed per unit length of filter thickness). Typically Schott publishes these values as the internal transmittance — transmittance without reflection losses at the surface — through a 1mm thickness of glass. Other manufacturers use 2mm as their reference. One can find the absorption coefficients by working backwards from this with the Beer-Lambert law. I also fitted a line to the refractive indexes given by the manufacturer, if two values were available. If only one refractive index was given, that was assumed to apply at all wavelengths. Using this info, it was then possible to get the complex refractive index, N, for each glass as a function of wavelength.

Using the complex refractive indexes, reflection coefficients can be calculated for each wavelength. Then the Transfer Matrix method described by numerous sources, including (C. L. Mitsas and D. I. Siapkas, 1995), (C. Katsidis and D. I. Siapkas, 2002), and (E. Centurioni, 2005), was used to calculate the transmittance for each wavelength. The light was assumed to be incoherent since these stacks don’t have any thin coatings that need a semi-coherent calculation. It was also assumed that the light was orthogonal to the stack. The filters are treated as uncemented with an air gap between, so there will be partial reflections in the gap (which are included in the calculation).

To calculate the metrics for safety and average transmittance, cubic hermite polynomials were used to interpolate the resulting transmittances at each wavelength, and then the integrals were performed analytically on the hermite polynomials.

References, Data Sources, and the Code

C. L. Mitsas and D. I. Siapkas. Generalized matrix method for analysis of coherent and incoherent re- flectance and transmittance of multilayer structures with rough surfaces, interfaces, and finite substrates. Applied Optics, 34(10), April 1995.

C. Katsidis and D. Siapkas. General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference. Applied optics, 41(19):3978–3987, 2002.

E. Centurioni. Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers. Applied Optics, 44(35):7532–7539, Dec. 2005.

Schott glass data (all URLs as of Nov 2, 2017)
http://www.us.schott...lass/index.html

QB21 (Newport Glass)
http://www.newportglass.com/opmcat.htm

U360 (Hoya)
http://www.hoyaoptics.com/pdf/U360.pdf

The actual code is here, and can be run by typing "compare_filterstacks" into the command window of MATLAB with this file in your current folder.
Code
Diabatic plotting routine (needed by the code)

Edited by Andy Perrin, 03 November 2017 - 07:11.


#2 Andrea B.

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Posted 03 November 2017 - 20:59

Andy, thank you heaps & bunches!

I have not yet read read it yet because we are in hyperactivity mode preparing for the chamber music society board meeting coming up this Sunday. This is also known as Andrea's Fall House Cleaning. :D AFHC requires locating the vacuum cleaner under all the piles of camera gear. No easy task! My reward is being first in line for the pumpkin spice cider donuts & champagne which will be served. :rolleyes:

So I will read it through with an editor's eye on Monday. Looking forward........




P.S. I gotta say it has been quite some time since I ever thought about splines and the various optics definitions you have used. Will it all come back to me ????? :wacko: :D

Yet another PS: It would also be interesting to make use of my tall stacks o' glass filtahs (lady you sure do gots some.....) and confirm the data with a practical experiment. I was surprised to see my often used 2+2 U-360+S8612 in the darker pink area. That stack has tested fairly IR proof (must go look up my experiments), although the lowered UV transmission does reasonably drag this stack downward. Hmmmmm........
Andrea G. Blum
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#3 Andy Perrin

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Posted 03 November 2017 - 22:58

Andrea, keep in mind we don't know what the minimum usable "Safety" value is. It may be that the practical cutoff is fairly low. Being in the pink just means that it is below the median of the stacks I tested.

Edited by Andy Perrin, 03 November 2017 - 23:01.


#4 Cadmium

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Posted 04 November 2017 - 02:51

First of all, Andy, this is excellent.
I have several points.
1) first of all, I have great difficulty reading the curves, because the colors are so close together. It might be easier to read if there were more colors used.
2) Schott has except data, and so does Hoya, although Hoya has ranges of data drop out in their data. However, I have not found the Chinese data to accurately represent true functionality of those glass types.
Your comparison is very amazing, however I don't trust QB21, QB39, ZWB1, ZWB2 graphs or data.
For example, I have compared stacks using various ZWB1 and QB21, QB39... which should have been comparable to Schott and Hoya equivalent stacks, but they didn't perform anywhere near the same.

And as I said, beware of data drop out ranges, like with the Hoya U-340 visual range.

Yes, my personal favorite stack is U-360 2mm + S8612 2mm, you can even use S8612 1.25, 1.5mm, or 1.75mm in that stack, and you will not usually see any problem, and it will make the stack exposure time a bit faster.
Safe Red/IR suppression starts at about OD 3.5, this can work fine, but for a more solid suppression I recommend OD 4.5+.
It depends on how strong you want that to be.
Like with the UG11 1mm + S8612 1.75mm stack, you may want to increase that to S8612 2mm, just to make it a bit stronger. I have seen some use only 1.5mm in that stick, and it works great, but this could depend on lighting too.

Another factor to consider when designing any UV stack, is that within the defined limit of the BG/S8612 type suppression glass, you will move the UV peak lower or higher with the thickness of the U glass.
For example, if you use the same U and BG glass, if you want a higher nm UV peak, then the U glass can be thinner and the BG glass be thicker, but if you want to move the UV peak to a lower nm,
then make the U glass thicker, and the BG glass thinner, within the the suppression OD required.
Two extreme examples:
UG11 1mm + S8612 1.75mm - Peak UV = 360nm
UG11 4mm + S8612 1mm - Peak UV = 347nm

The transmission depth of the lens will truncate the effective lower UV transmission range, and can also change the UV peak nm position.
This is why with most UV capable lenses, other than the very expensive specialized lenses, such as UV-Nikkor, Coastal Optics, etc., the U-360 + S8612 stacks will work best.

Edited by Cadmium, 04 November 2017 - 03:09.


#5 Andy Perrin

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Posted 04 November 2017 - 03:52

Cadmium, the curves were more to give an overall impression of how the progression went, rather than intended to be individually readable. (If individual readability is desired, I can just make separate graphs for each one, which is not much additional work.) I am considering separating them into groups based on how the stacks cluster on the Transmission-Safety graph, which might help. Also, it is a good point about the peak value. That is a third attribute I could look at, and make some additional plots.

Edited by Andy Perrin, 04 November 2017 - 03:53.


#6 Cadmium

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Posted 04 November 2017 - 07:18

I like that word, attribute.
Of course the first two attributes that come to my mind when building a UV stack are,
1) UV transmission peak % (amplitude), and
2) Red/IR suppression OD (optical density), or 1E03 to 1E05-
Then I suppose the nest one that comes to mind is
3) UV transmission band width, also
4) UV peak nm, and
5) UV/Blue cutoff edge nm.
The only other one I think of at the moment, might be
6) Peak roundness.

I still stress to those who are getting intro this that the lens is critical. Other than specialty UV lenses costing thousand of dollars,
all 'accidental' UV capable lenses have a UV drop off curve, which superimposes itself on the filter curve,
and defines the lower limit and profile of the UV band. Thus truncating the lower limit and curve of the UV filter transmission.
This is why U-360 is my favorite U glass. It is functionally better than UG1, although this is not seen by comparing their two graphs.
In fact, I think U-360 cuts more blue than UG1 does at the same thickness, but the data doesn't show that.

I really like your graph. I just think that adding more colors would help differentiate the types of glass,
because I keep looking for the Red/IR OD suppression of one or another in the list, but I can't pick that out on the graph, to see what OD is has,
or follow the line to the UV range to see what the corresponding curve looks like there.

Edited by Cadmium, 04 November 2017 - 07:25.


#7 Andy Perrin

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Posted 04 November 2017 - 11:43

Cadmium, I can put the OD number on the top graph, or I can simply make a different one. The OD suppression is the red area on the graph essentially but looking at that is misleading because we really care about the RATIO of UV to IR not the total amount of IR alone. This is why I defined the Safety.

#8 Andrea B.

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Posted 07 November 2017 - 05:53

Andy, thanks for including some references!

*****

I am wondering if there needs to be some discussion of the UV illumination assumptions? That is, other than the assumed orthogonality of light to filter and the reflection comments.

For example, outdoors in strong summer sunlight at noon which is rather overloaded with IR light, any UV-pass filter having IR "leakage" will perform a bit worse (i.e., possibly produce more of that "IR washout" look in a photo) than it would if used indoors in low ambient light with filtered UV-Led or UV-Flash illumination. So that sunny day scenario might deserve some heavier weighting of the IR contribution to Safety than would a very low IR indoor scenario? Of course, the net effect (I think??) of a heavier IR weighting would be a "shifted" placement relative to the existing chart, so maybe it is not so important to actually attempt this weighting idea for different UV illumination because the Safety is best interpreted as a relative measurement rather than an absolute one. B) :wacko:

Well, I digressed into that because I've been very concerned recently that folks forget to take into account their lens performance and illumination content when looking at all the glorious perfection of UV-pass filter transmission charts. :lol: We are rarely able to capture all the light under those curves in typical UV photography even when using UV-dedicated lenses.

ADDED LATER: I'm only suggesting adding one sentence to the write-up to remind readers that actual results may vary due to the UV/IR content of the illumination in use. I.e., that you are assuming "perfect" UV/IR illumination.
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#9 Andrea B.

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Posted 07 November 2017 - 06:16

I was noticing the following.... The 2mm UG11 with increasing S8612 thicknesses, plots along a line with negative slope. [[Same for the 1mm UG11 with increasing S8612 thicknesses.]] But the 2mm U-360 with increasing S8612 thicknesses plots along an almost vertical line.

Thus increasing the S8612 thicknesses only serves to lower UV transmission in the U-360 glass and does not change the U-360 safety. For the UG11, as UV transmission is reduced, safety is increased.

Did I interpret that correctly? Why would these two UV-pass glasses not have similar responses to the S8612 glass?
Andrea G. Blum
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#10 Andrea B.

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Posted 07 November 2017 - 15:47

Added later: My 2nd question is the most important one. Why does that U-360 not improve its IR blocking with increasing S8612 thickness?

My 1st comment about illumination is minor. The suggestion is simply to add one sentence that reminds readers that actual results may vary in practice. That readers should already know this true, but we still should practice good reminders, yes?
Andrea G. Blum
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#11 Andrea B.

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Posted 07 November 2017 - 15:51

Third Comment: It might be interesting to see the plotting on the chart of the unblocked UV-pass substrate.

Fourth Comment: How does the IR Safety Ratio compare to the OD value of the stack? Reasonable to ask.
Andrea G. Blum
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#12 Andy Perrin

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Posted 07 November 2017 - 16:01

Andrea, last question is easiest. Others will be saved for when my work calms down a bit and I have time to do a complete revision of this project! I want to incorporate everyone's suggestions.
--
The Safety is a signal-to-noise ratio, where signal is the UV content of the light that passes the filter, and noise is everything else that passes. The OD is a measure of JUST the noise. The case I'm making is that we really care about the ratio of the UV to IR, the Safety, not just how much IR is blocked. It may be (I don't know yet!) that using either measure gives the same end results, but that's on my list of things to check for the revision.