Digiscope Calculator Ver. 1.4p
By Jay Turberville
October 27, 2003
Last Revised October 11, 2007
The calculator is divided into two main sections. The first section is used to enter in camera, scope and eyepiece information and the second section is used to calculate effective digiscoping information. The basic operation is simple. Once the appropriate camera, scope and eyepiece information is entered, you simply click the "Calculate Digiscoping Data" button on the second portion and all of the calculations are performed.
These instructions are also divided into two parts. The first part is a "quick start" and will be sufficient for most people to get going. The second part is a item by item description of each data field and button function.
If your camera and scope are in the pulldown lists, then it will be pretty easy to use these brief instructions. If not, you may have to read further.
The calculator opens up with the default values for a CP4500 camera and a Swarovski ATS80HD scope. The default scope magnification is set at 20x. The default camera focal length is set at 18mm. And the default f-number is set at f4. These default settings are somewhat arbitrary and are the variables that will probably want to change.
For instance, if you are trying to determine the maximum possible 35mm equivalent focal length for your scope and camera, you would change the "Scope Magnification" and the "Camera Focal Length" before calculating the digiscoping data. Given a specific camera and scope, these are the two values you will most likely be changing. If you also wanted to see what effect the camera aperture would have on a variety of factors, you might also enter in a different "Camera f-number".
All of the data fields will allow you to enter in information for different cameras and scopes. These can be real or imagined. For instance if you wanted to see what advantages a 100mm aperture scope would have over your 80mm, you could simply enter in the new aperture value and calculate the results. But I suggest reading the detailed info on each data field and calculation button before doing this type of experimentation.
Be careful when entering values to be sure that you have completely overwritten the previous values. It is very easy to find that you simply appended your new value to the old value. You can easily find yourself with a ridiculous "Scope Magnifaction" of "2030" if you are not careful.
A value of "NaN" in field indicates an error of some sort. It literally means that the data generated is "Not a Number". Odds are that there either is no data entered in a field or that some non-numeric character was erroneously entered somewhere.
Quick Start - Camera only
Pick a camera. Choose "No scope - camera only)" for the scope. This sets the scope magnification to 1 which eliminates the scope as a factor. You can now click the "Calculate Digiscoping Data" to generate lp/mm and related information.
If you want to do some "what ifs" for camera design, simply select from the list of sensor sizes. The CCD diagonal, equivalent focal length and camera FOV will be calculated when a different sensor size is chosen. You can type in different horizontal and vertical pixel values and then recalculate using the Calculate FOV and Calculate CCD buttons.
You can vary the camera's f-stop and see how this effect the limits of resolution due to diffraction by clicking the Calculate Digiscoping Data button. You can compare those numbers to the lp/mm limits imposed by the sensor.
Pick a Camera - Populates all camera data for listed cameras. I somewhat arbitrarily chose a 50mm lens for the DSLRs since they have interchangeable lenses.
Pick a Scope - Populates the "Scope Aperture" and "Scope Focal Length" fields as well as the "Scope Magnification" field. It is likely that the "Scope Magnification" field will not have the value that you want. I simply picked defaults for some of the more popular eyepieces.
Scope Aperture - The effective objective diameter of the telescope.
Eyepiece Focal Length - This value can be entered or calculated. If you enter a value, you can calculate the "Scope Magnification" by clicking the "Calc Scope Mag. from Eyepiece FL" button. It is not necessary to have a value entered here.
Scope Magnification - This value can be entered or calculated (see above). If you enter a value, you can calculate the "Eyepiece Focal Length" by clicking the "Calc Eyepiece FL from Scope Mag." button. This value must be entered to get valid digiscoping data.
Calc Eyepiece FL from Scope Mag. - Calculates the "Eyepiece Focal Length" using the "Scope Magnification" and "Scope Focal Length values.
Calc Scope Mag from Eyepiece FL - Calculates the "Scope Magnification" using the "Eyepiece Focal Length" and "Scope Focal Length" values.
Scope Focal Length - The focal length of the scope.
Camera Focal Length - The camera focal length that you want to use in the digiscoping calculations. This value should the same as either of the camera's minimum or maximum focal lengths or some value in between. This value plays an important part in calculating the Digiscoping Data.
Camera f-number The f-number of the camera lens. This may or may not be used to calculate the , "Effective f-number", "Effective Scope Aperture" and theoretical optical resolutions.
Horizontal Camera Pixels - The number of horizontal pixels generated by the camera.
Vertical Camera Pixels - The number of vertical pixels generated by the camera.
Camera Min & Max Focal Length - The focal length range of the camera's lens. These values are used along with the CCD diagonal length to calculate the "Camera Max & Min FOV". The Max Focal Length value is used when calculating the "CCD Diagonal & Pixel "diameter" values.
Camera Min & Max 35mm Equiv Focal Length - The approximate 35mm equivalent focal lengths that would provide the same FOV as that resulting from the camera's actual focal length and CCD diagonal.
Camera Max & Min Diag. FOV - The actual Field of View (FOV) of the camera across the diagonal of the CCD. This is useful when considering how an eyepiece's AFOV might match up to the camera's range of FOVs.
Calc Camera FOV - Calculates the camera's FOV if valid values for the, "CCD Diagonal", "Camera Max Focal Length", and "Camera Max 35mm Equiv Focal Length" are entered.
CCD Diagonal & Pixel "diameter" - The CCD dimension across its diagonal and the theoretical dimension of an image pixel if overlayed onto the CCD. The actual sensors are physically smaller. Both values can be calculated using the "Calc CCD" button.
Calc CCD - Calculates the "CCD Diagonal" value, "Pixel diameter" value, and "Megapixels" value. The "Camera Max Focal Length" and "Camera Max 35mm Equiv Focal Length" must be entered to generate a value.
Camera Notes - Notes on cameras and how effective they are for digiscoping. Some of this info is very well founded and some is speculative. I will update this info as I read reports of other people's experiences. Of course, I'll use my own experience as well.
Calculate Digiscoping Data - Calculates the "Digiscoping Data" based on the values entered in the first section of the calculator.
Actual Digiscoping Focal Length - The actual optical focal length calculated from values for the combination of scope, eyepiece and camera lens.
Digiscoping 35mm Equivalent Focal Length - The equivalent 35mm focal length that would be needed on a 35mm camera to yield the same camera FOV.
Camera FOV - The field of view of the camera alone at the specified "Camera Focal Length".
Digiscoping FOV - The field of view through the camera of the scope, camera, eyepiece combination.
Camera Aperture Diameter - The physical diameter of the camera lens aperture. Useful for comparision to the "Scope Exit Pupil".
Scope Exit Pupil - The diameter of the scope's exit pupil. Useful for comparison to the "Camera Aperture Diameter".
Effective f-number - The actual effective f-number of the scope, camera and eyepiece combination. This number can never be smaller than the "Camera f-number" but can be larger. It is larger when the "Scope Exit Pupil Diameter" is smaller than the "Camera Aperture Diameter". It is also worth noting that this value can smaller than the f-number for the scope being used. This can occur when the "Actual Digiscoping Focal Length" is less than the "Scope Focal Length". In this case, the eyepiece and camera lens effectively act as a "focal reducer". This can be readily seen when the f10 LZOS Rubinar is used at 20X magnification.
Effective Scope Aperture - When the "Scope Exit Pupil Diameter" is larger than the "Camera Aperture Diameter", then the camera's aperture will partially occlude it. This effectively reduces the scope's aperture diameter and limits the "Best Theoretical Optical Resolutions".
Best Optical Resolution Rayleigh (lp/mm) - This is the best theoretical resolution possible with the digiscoping combination assuming the entire assemblage was diffraction limited. Bear in mind, however, that it is extremely unlikely that such is the case. This calculation is base on the Rayleigh criteria and is calculated using the following formula:
Rayleigh limit (line pairs per mm) = 1/(1.22*N *W )
where "N" is the "Effective f-number" and "W" is the wavelength of green light (0.0005mm is used). The "line pairs per mm" refer to the line pairs as imaged at the CCD. This is a useful number if you shoot resolution tests using lens charts that use this metric. I use the lens charts found at http://www.normankoren.com/Tutorials/MTF5.html. Keep in mind that the Rayleigh criteria relates to an MTF of about 9%. Read more about what makes an image appear sharp at the Norman Koren website.
Maximum CCD Resolution - This is the maximum possible resolution that the CCD could provide assuming it had red, green and blue sensors at all sensor locations. Right now the Foveon sensor is the only sensor with this capability. This is also the CCD resolution implied by the sensor's physical dimension and the horizontal and vertical camera pixels that the camera delivers. The actual resolution possible is somewhat less than this when a Bayer Mask is used (as is usually the case).
Best Optical Resolution Rayleigh (degrees)- The same as the "Best Theoretical Optical Resolution (lp/mm)" except expressed in degrees.
Max CCD Res Bayer Mask adjusted (lp/mm) - CCD sensors using a Bayer Mask will not deliver quite the resolution that their sensor count implies. The camera uses interpolation techniques to derive R,G and B color information for each pixel from surrounding pixels. The result is a small reduction in resolution. I've used my own testing and information from
http://www.normankoren.com/Tutorials/MTF7.html to come up with the estimate that my Nikon Coolpix 995 and Coolpix 5000 both deliver about 80% of the "Maximum CCD Resolution". I suspect this will be similar for most digicams.
Best Optical Resolution 10% MTF - MTF (Modulation Transfer Function) is a concept that refers not only to the ability to resolve detail, but also refers to how accurately the detail is recorded. When we take a picture of black and white lines on a test target, the black and white lines usually aren't as black or white in the image as they were in reality. The finer the line width and spacing, the more their values move toward middle gray. And the limit of resolvability is when they kind of mush together as both types of lines are become gray and indistinguishable from each other. The MTF value represents how accurately these lines are recorded. 100% means "perfect". The black is as black and the white is as white as on the original. 50% means that the black and white lines have moved halfway toward the 50% gray value. They have 50% of the contrast of the original. And 10% means the lines are almost the same gray value. The Rayleigh resolution criteria equates to about 9% MTF. If you find this interesting, you will really love this site:
*Best Optical Resolution 50% MTF - See the explanation of MTF above. 50% MTF is significant because it is very closely correlated to the human perception of sharpness. A lens can resolve a lot of detail, but if it is resolved at MTF values lower than 50% MTF, it will be perceived as correspondingly less sharp. So the point where a lens fails to deliver 50% MTF or better is important. It will take some testing to verify this, but I suspect that when the 50% MTF lens resolution is lower than the CCD's Bayer Mask adjusted resolution, we can expect to start seeing a "softer" image. But even though this image may be softer, there is certainly detail recorded at resolutions higher than the 50% MTF. Sharpening an image increases the image's MTF response. It does not increase, however, increase the amount of detail in the image. The detail was either recorded or it was not. Sharpening can increase the contrast in what detail that is recorded and thereby alter the human perception of sharpness. For a typical catadioptric with a 40% obstruction, this value indicates something closer to a 35% MTF value
Calculate Distance to Subject - Sometimes it may be interesting to derive a good estimate of how far away a bird or other subject was. This button and section allows you to make reasonable estimates. If the subject dimension and digiscoping data is very accurate, then this estimate will be similarly accurate. Click this button to perform the calculations once you have entered the "Dimension of the Object" and the "Pixel Dimention of the Object".
CCD Diagonal - This value should already be present if you have completed the first portion of the calculator and then clicked the "Calculate Digiscoping Data" button.
Dimension of Object - The dimension of the object as it appears in your photograph. For instance, if you were using an image of a person standing erect and you knew that person to be 6 feet tall, then you would convert 6 feet into meters and enter in that value. If your image was of a bird, then you can use bird length and or wingspan ranges for the species to estimate a value. Remember to consider the degree that the subject might be angled toward or away from the camera when making these estimations. Subjects that are very nearly parallel (in the direction you are measuring) to the camera's focal plane (CCD) are best.
Pixel Dimension of Object - This is the number of pixels (at full image resolution) that span the object being used. Using the 6 foot tall person example again, this would be the number of pixels that span the image from the top of the person's head to the bottom of their feet. I use Photoshop's "Draw Rectangle" tool and the "Info" window to measure this directly on the image. If the object in question is at an angle (as is common with a perched bird), then I rotate the image so that the angle is horizontal or vertical and then make the measurement.
Calculated Distance to Subject - This is the calculated distance. As stated above, the accuracy of this estimate will depend greatly on the accuracy of the input data.
About the Calculator
This first version of the online calculator gives the core calculations that I found myself using most frequently. It also has an additional feature that allows you to estimate camera to subject distances fairly accurately if you have a good idea of the size of the subject in your image. I initially added this feature to my copy of George's spreadsheet for the "gee whiz" factor. But later I found that it was useful in determining that atmospheric disturbances tend to affect digiscoped images at distances greater than about 50 meters. So getting a good feel for subject to camera distances can be useful and this may actually help that process along a bit.
This calculator gives resolution values in line pairs per millimeter (lp/mm) to make it easier to compare theoretical results with actual results obtained from test targets. Specifically, I use Norman Koren's test targets that can be downloaded from http://www.normankoren.com/Tutorials/MTF5.html - another excellent site (though focused on photography in general and not digiscoping in particular). It was also found that George's original resolution calculations were off by a factor of two (something pointed out by someone on the Yahoo Digiscoping Birds forum). This online calculator does not have this error. However, it is interesting to note that the erroneous values that George's original spreadsheet gave were very good predictors of actual digiscoping performance. This is strong evidence that we are not dealing with an optical combination that is diffraction limited when we digiscope. In the meantime, be aware that it is unlikely that you will actually get image resolution near the theoretical limit. For now, it seems safe to assume that a digiscoping rig will deliver between 50% and 75% of the theoretical resolution calculated.
Version 1.1 (12/06/03) added buttons for presets and made the calculator a bit more compact vertically.
Version 1.2 (12/13/03) removed ugly buttons and replaced them with select lists. Added more presets for a greater variety of scopes. Magnifications for scopes are fairly arbitrary since many eyepieces are available. I had a difficult time locating focal lengths for Nikon and Kowa scopes. Feel free to email me with good technical specifications for any cameras or scopes that you would like to have me include in the list.
Version 1.3 (01/03/04) More entries on select lists added since 12/13/03. Added info for camera minimum zoom values. Also added calculations to provide camera FOV values for these minimum and maximums. Added some quick instructions and detailed descriptions of the calculator fields and functions. Removed the instructions embedded in the calculator interface and modified the naming of some of the buttons and fields for better formatting.
Version 1.4 (01/14/04) Added the 50% MTF and 10% MTF fields. Camera notes and more cameras were added in a later version of 1.3, but I'll mention their addition here. I also adjusted the wavelength of light used in calculating resolution limits from 0.00055 to 0.0005 to be consistent with the calculations on Norman Koren's site. The difference is small, but there seemed to be enough pointers suggesting that the 0.00055 value was a bit more pessimistic than it should be. Its does not shift the values much, but it does shift them.
Version 1.4a-d (05/21/04) Have added various scope and camera values over that past few months as they seemed appropriate.
Version 1.4e (07/17/04) More camera and scope values added including a "No Scope" option to simplify camera only calculations. Added a sensor size pulldown and data. Megapixels are now calculated when a camera is selected or when the CCD calculation is made. These modifications should help with camera "what if" calculations.
Version 1.4f (08/28/04) More cameras added and the sensor selector was modified to fully calculate equivalent focal lengths, CCD diagonal and pixel pitch when selected.
Version 1.4g (01/01/05) Added the Nikon D70 and Kyocera SL400R as well as two TeleVue scopes, the Celestron C5 and the Astro-Physics Traveler. Added a note about the 50% MTF value when considering obstructed catadioptric scopes. Dropped the old camera table.
Version 1.4h (01/21/05) Modified calculation for Digiscoping FOV. The previous calculation was very slightly off due to the use of an incorrect and overly simle formula.
Version 1.4i(03/17/05) Added three cameras. The Sony DSC-W1, Sigma SD10 and Olympus E300.
Version 1.4k(12/08/05) Added more cameras. Canon 5D, Nikon D200, Sony DSC-R1
Version 1.4l(11/12/06) Added Zeiss Camera-Eyepiece DC4, Sony DSLR-A100, Nikon D80, Canon EOS 400D, Sigma SD-14
Version 1.4M(05/05/07) Added William Optics ZenithStar 66 SD APO telescope.
Version 1.4N(05/09/07) Added Nikon P5000 10Mp Compact digital camera.
Version 1.4P(10/11/07) Added Nikon P5100, FujiFilm F30, F31fp, F20 and E900. Also updated the Nikon DSLRs to reflect the newer cameras added. These are now grouped under the same camera when the cameras have the same sensor size and pixel count. Added new Leica Televid 65 and 82 scopes as well as the Swarovski ATS65HD.
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Copyright © 2003 by Jay Turberville