Tuesday, December 8, 2009

Math and Photography

Some of the most common questions I get on the flickr photography forum are related to filter use.

I plan on creating multiple filter tutorials over the winter and will blog and post them to my website. In the meantime, I will briefly touch on using the B+W ND 3.0 10 stop neutral density filter.

Using neutral density filters as strong as the B+W 10 stop requires a few steps and a little math.

First, the filter is so dark, it is next to impossible to compose an image with the filter in place. Therefore, it is important to compose your frame, focus, and calculate a proper exposure prior to adding the 10 stop filter. For the image above, I also was using a Singh-Ray Gold-N-Blue polarizer and a Lee .75 Soft GND (graduated neutral density filter). The polarizer helped create the intense gold and blue tones in the image, and the GND helped reduce the light in the sky to better balance the image's dynamic range.

Like I mentioned before, I composed, focused, and fired off some test shots with all my filters attached but without the 10 stop filter. This is where the creative and visual approach I choose for my photography comes in...and a little math.

Depending on the look I am going for, and how fast the clouds are moving, I may choose to expose a scene between 30 seconds and several minutes. On this day I tried shots between 30 seconds and 2.5 minutes, with around a minute being the length of shutter speed giving me the cloud movement I wanted.

Now, onto the math. I typically shoot my landscapes at the base ISO of my camera for quality purposes, in this case ISO 100. I also often start my calculations for shutter speed with my aperture set to give me a good depth of field, typically f16. For this photo, I came up with a shutter speed of 1/4 second.

Adding in 10 stops of light reduction, meant that I needed to increase my shutter speed by 10 stops as well. A halving (or doubling) of a shutter speed is one stop of light. Therefore:

1/4" > 1/2" = 1 stop
1/2" > 1" = 2 stops
1" > 2" = 3 stops
2" > 4" = 4 stops
4" > 8" = 5 stops
8" > 15" = 6 stops
15" > 30" = 7 stops
30" > 1' = 8 stops
1' > 2' = 9 stops
2' > 4' = 10 stops

This would mean a 4 minute exposure would be needed! This is much longer than I wanted to shoot as the clouds would have lost all detail. Not to mention hand holding my GND for that long is tiresome.

So what can I do to need less light, and therefore less time for a shorter exposure? First, I changed my camera's ISO to 200. This gave me a full stop back. Now I could shoot for 2 minutes. I also knew that by changing my aperture to allow more light would help.

Aperture settings (f-stops) in full stops.
1 – 1.4 – 2 – 2.8 – 4 – 5.6 – 8 – 11 – 16 – 22 – 32

From my days of shooting film, my lenses had most of these settings, especially f2.8 - f22. Now, with digital, most cameras can electronically change the aperture in 1/3 stop increments. For example, between f8 and f11, I now have f9 and f10 as options. And between f11 and f16, I now have f13 and f14.

For this image, I opened my aperture to f13, knowing I would retain a good depth of field and gain a 2/3 stop of light (compared to f16) at the same time. Since a full stop (at f11) would have meant shooting at 1 minute even, 2/3 stop (at f13) equates to 40 seconds, or 2/3 of a minute. My calculated shutter speed for ISO 200, f13 and all my filters was 1 minute, 20 seconds by opening my aperture from f16 to f13.

As is often the case, I forgot my stop watch and phone in the car, so I just counted in my head. I was 10 seconds short, but in the end, that is not much of a difference.

By changing both my ISO and aperture to settings within reason for good image quality, I was able to get a long shutter speed, but not too long. Like I mentioned previously, how long is based on variables that I evaluate in the field.

I encourage you to ask any questions here on the blog, and if any of my math is incorrect, please let me know, and I will correct it.


  1. Very nice image and great info on your process in taking this image.

  2. Very inspiring, I think I'm going to learn a lot from you. Will be eagerly awaiting you next posts. Thanks.

  3. Have you heard of the Singh-Ray variable ND filter? I haven't used it, but I believe it goes to 10 stops, but also allows you to dial in just what you want, from 0-10 stops. So you can compose your shot, then dial in the ND and let your meter do the math.

  4. Thanks guys, and John, yes, I have heard of the Vari-ND. In fact, I own one. I have the standard mount, so I can screw a polarizer into the front. That being said, the Vari-ND is quite large and I often need to zoom in to about 15-16mm on my 12-24mm lense to avoid vignetting. It also is only variable from 2-8 stops with 8 stops pushing the boundaries of getting the cross hatching that Singh-Ray's site talks about. A great tool, but not when you want to shoot super wide.

  5. Thanks for such a magnific picture and rich explanation. I am myself considering to buy a B+W ND 3.0. But I am wondering if the Hoya ND400 is a better option. The Hoya gives you only 9 stops, but it is multicoated and, for what I have read, the color cast is less intensive. I have noticed that your girlfriend Kendra uses the Hoya. Have you maybe compared both filters and would recommend one of them? Thanks a lot.

  6. Thanks Jim for the breakdown, I now understand alittle bit more but not quite there yet. I usually guess the exposure time when using my 10 stop however this dose not tend to get me the best of results!
    This info is very useful indeed.

    Have you tried using a Lee filter holder with just 1x slot with a WA ring to go in front of your 10stop? I use one on my 17mm lens on a full frame body and I don't get any vignetting.

  7. Jim,
    I am assuming this is a digital image. Does the pick up not suffer the way film does from reciprocity faliure? I am new to digital and have not played with extended exposures.
    Very nice image. The sky is wonderful.


  8. Beco, I have used both, and to be honest, the color cast seems to be about the same. Both are easily corrected with the custom white balance tool in ACR (or other photo editing programs with a custom white balance tool, like Nikon's Capture NX).

    Reed, yes, the Lee holder with one filter works fine, and often is fine with more than one GND filter installed. It is when thicker screw-in filters are installed that I cannot use the widest focal lengths of my 12-24mm lens.

    Jim, yes, this is a digital image and thanks for exposing me to a new term. As I understand it, reciprocity failure is more a concern with long exposures with film. Digital noise is the bigger concern for long exposures with digital cameras.

  9. You have the VariND? I can't recall seeing you post a shot where that filter was used.

  10. Lukas, it has so much vignetting, that I don't reach for it all the time, but I am using it more and more. I have some shots from Tahoe that I haven't posted where I used it.

  11. A very great tutorial in analyzing exposure. This will be a great help for me since I am starting with landscape and photography. I hope I can freeze the light while doing the calculations.. haha :D Thanks for sharing your experiences. More power to you..

  12. Thank you for sharing you work and your knowledge you have. I saw your article on singh ray blog about Gold-B-Blue filters. It's also great.

    If you don't mind, I'd like to invite you to my blog..Happy New Year..

  13. Your photos are incredible! I mean it! Thre is something from a fairy tale in them:)Not to mention the multitude of information You share with us... Thank you!

    I also invite you to my blog:)

  14. Great tutorial, amazing images. Thanks

  15. congratulations!!! extraordinary photographs!!!
    and very interesting tutorial. thank you!

  16. Awesomeand thank you however I'm looking forward to the filter tutorials that you mention onthis blog, please if you find the time I'm sure small snippets would be great too.

  17. One comment on doing the math quickly. 10 stops is a factor of 1000, so read the shutter speed without the filter, convert to decimal and multiply by 1000. That you can do in your head. E.g. in your example 1/4 sec = .250 sec ->250 sec with the filter (4 minutes).
    --Bruce Silver

  18. Bruce, thanks for that comment. It certainly works and is a quick way of converting the time.