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Tutorial: How many pictures I have to do to an stack?

Posted by Fernandez Oscar  
avatar
Fernandez Oscar November 12, 2013 12:23AM
Hi to all,

I write this article originally in spanish, my English is very bad so I apologize for my translation...

What I will say is not new but it is a great help to those who are introduced in the extreme macro by a macro focus rail and using software.

This is a question many have made me and that I had to answer me when I started doing extreme photos. Everyone goes through several steps to find out what the magic number of pictures you have to do to make a program stacking properly perform the calculations and we present a crisp image without loss of focus or blurry bands for not having properly photographed.

In my personal experience I think there are at least three ways of knowing how many pictures we have to do:
 
1. - Test / Error. It's the way that I think we all started. We do many tests until we get more or less a decent result. Then aim few pictures we needed per millimeter and from there continue taking pictures.
 
This system is entirely feasible, but not necessarily valid and correct, we can addict to commit mistakes and repeatedly.


2. - Experience. Very close to the former, lies to get used to quickly handle zoom we're working on an approximation of how many pictures I will need. This method is completely valid but we can fall into the trap of making too many or few photos.
 
In many cases we rely on measures, FOV, etc.., For calculations.


3. - The scientific method. Is more complicated because need a formula to be used but the most correct with respect to cover the mineral or the gem. Let's do an overview of what we want ...
 
We're talking about studio picture with an focus line or similar which moves the gem or the camera, either vertically or horizontally. If you are sure that the movement is constant the success is almost assured. Because we have an object too close to the camera lens our depth of field is very small.
 
It's like our eyes look a finger of your hand within 3 cm, forces us to get crossed and we are only able to focus a little. If you move away a little, I hardly have to get crossed and we are able to see a little more of the object. If further away we no longer have to put focus squint and almost completely. A little further and you focus it perfectly (i hope understand my example, sorry for my english).

For the case that concerns us is very similar. The depth of field you have to shoot a very small so close makes it only a "slice" focus of our mineral and the rest out of focus, both forward and backward. If unite all the slices whole in this case is the mineral.
 
Our work then lies in cutting the right size for each slice in the end we have our perfectly focused.
 
Now on to one of the formulas used to calculate the depth of field we have in each photograph. This formula is the call of Lefkowtz which is expressed as:
 
DOV or distance CoC * = 2 * f * ((m +1) / (m * m))

CoC is the Circle of Confusion, but we'll talk later than the given data is basically a camera for each model and the manufacturer, where we indicate when a point is totally focused. If you want to see a list of these values ​​you see in the list of the end of this post.  
f is the opening. For example 5.6 which is a widely used value.
 
m is the magnification or zoom factor used. To calculate this value you can check in the list. 
 
I'll put two examples of use of microscope objectives. In the case of the aperture (f) for a normal lens can change it manually or through the buttons on the camera, with which the selected value would be the value of f. But in a dependent microscope objective aperture NA is given by the manufacturer and is fixed. However, to make use Lefkowtz formula must apply before the following formula:
 
f = 1 / (2 * NA)

Now let's see the first objective microscope, Nikon BD Plan 5x known with an optimal distance of 210mm and 0.1 NA.
 
After applying the above formula the value of the opening would be f = 1 / (2 * 0.1) = 5
 
 
Now let's calculate the appropriate distance for this purpose working 5x:
 
CoC distance * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 5 * ((5 +1) / 5 * 5) = 2 * 0.019 * 5 * 0.24 = 0.0456 mm
 
That is, the ideal displacement should do between shots is 0.0456 mm but not yet finished. This would be ideal, but movement could occur at each slice approach as closely if unnoticed each of these with a thin lonchita unfocused therefore used to ensure an overlap which is usually between 20 to 30%. In my case I've always applied the 25% when I use the formula. Then then the thing would look like:
 
CoC distance * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 5 * ((5 +1) / 5 * 5) = 2 * 0.019 * 5 * 0.24 = * .75 = 0.0456 mm 0.0342 mm distance to move between photos.
 
With this we have covered all the movement we have to do. This leaves roughly 30 pictures per millimeter for this purpose and 5x.

If we have for example a screw with a displacement per revolution of 1mm and a relationship between the spindle and the motor by a pulley / belt 3:1 this means that we have the following resolution in our approach lane:
 
1mm revolution / engine 200 steps / 3 = 1/600 = 0.001666666666666 microns per step motor. Then we indicate our 36 degrees program to rotate or what is the same, 20 steps.
 
Of course these values ​​will depend on your approach lane.
 
As this objective also use it at 2, 3 and 4x going to put the calculations:
 
4x distance CoC * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 5 * ((4 +1) / 4 * 4) = 2 * 0.019 * 5 * 0, 3125 = 0.059375 mm * 75 = 0.04453125 mm distance to move between photos = 46.80 º
 
3x distance CoC * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 5 * ((3 +1) / 3 * 3) = 2 * 0.019 * 5 * 0, 444444444 = 0.0844444 mm * .75 = 0.0633333 mm distance to move between photos = 68.40 º
 
2x distance CoC * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 5 * ((2 +1) / 2 * 2) = 2 * 0.019 * 5 * 0, 75 = 0.1425 mm * .75 = 0.106875 mm distance to move between photos = 115.20


Now let's do the same with the other goal, a Nikon E Plan 10x with an optimal distance of 160mm and 0.25 NA. This goal usually work at 6x, 8x, 10x and 12x. The value of f is:
 
f = 1 / (2 * 0.25) = 1/0.5 = 2
 
6x distance CoC * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 2 * ((6 +1) / 6 * 6) = 2 * 0.019 * 5 * 0, 194444 = 0.01477777 mm * 75 = 0.01108333333 mm distance to move between photos = 10.80 º
 
8x distance CoC * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 2 * ((8 +1) / 8 * 8 ) = 2 * 0.019 * 5 * 0, 140625 = 0.0106875 * .75 = 0.008015625 mm distance to move between photos = 7.20 º
 
10x distance CoC * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 2 * ((10 +1) / 10 * 10) = 2 * 0.019 * 5 * 0, 11 = 0.008360 mm * .75 = .00627 mm distance to move between photos = 5.40 º
 
12x distance CoC * = 2 * f * ((m +1) / (m * m)) = 2 * 0.019 * 2 * ((12 +1) / 12 * 12) = 2 * 0.019 * 5 * 0, 090277777 = 0.0068611111 mm * .75 = 0.005145833333 mm distance to move between photos = 5.40 º


Now we know what we must move on each picture and therefore, as we know the starting point and end point of the crystal, gem or mineral to photograph, we can divide this total distance in number of millimeters that we must move to meet our goal successfully.
 
 
However, now let deepen a little more in the CoC or Circle of Confusion. Some people prefer that this value is not a constant but a variable value is not dependent on what the manufacturer says the resolution but we are working. So you can define the following formulas to calculate the appropriate value:
 
- CoC pixels = 3 to the value the user tolerated as valid. But there's usually three specialized values that the users who prefer to use values ​​such as 2, 4 or 5.
- Pixel size in millimeters = Square Root of (Width * Height Sensor sensor / Number of pixels)
- CoC CoC mm = pixel * pixel size in millimeters

We will apply these formulas to my EOS 600D:
 
Canon EOS 600 D. Sensor size = 22.3 mm * 14.9 mm. Number of pixels = 5.184 * 3.456
Pixel size in mm = SQRT ((22.3 * 14.9) / (5,184 * 3,456)) = 0.004306517
CoC mm = 0.004306517 * 3 = 0.013 which is different from what the manufacturer says 0,019
 
So if we meet or approach to what the manufacturer says would be multiplied by a little more than 4.44
 
I however prefer to stay with the CoC value provided by the manufacturer, once applied value one two points consistent with this third point.
 
 
Hope you have not been a bummer all and have will be useful to some.
 
Regarding stacking which program to use, I think this comparison of results and timing is critical: http://www.gemologyonline.com/Forum/phpBB2/viewtopic.php?f=57&t=18489
 
Regards, Oscar.

Table of CoC and Sensor sizes:
------------------------------
Canon EOS-1D C (*) 36 x 24 0.023
Canon EOS-1D Mark II 28,7 × 19,1 0.023
Canon EOS-1D Mark II N 28,7 x 19,1 0.023
Canon EOS-1Ds Mark II 36 x 24 0.030
Canon EOS-1D Mark III 28,1 × 18,7 0.023
Canon EOS-1Ds Mark III 36 x 24 0.030
Canon EOS-1D Mark IV 27,9 x 18,6 0.023
Canon EOS 1D X (*) 36 x 24 0.030
Canon EOS 5D 35,8 x 23,9 0.030
Canon EOS 5D Mark II 36 x 24 0.030
Canon EOS 5D Mark III (*) 36 x 24 0.030
Canon EOS 6D (*) 36 x 24 ¿?
Canon EOS 7D 22,3 x 14,9 0.019
Canon EOS 20D 22,5 x 15 0.019
Canon EOS 30D 22,5 x 15 0.019
Canon EOS 40D 22,5 x 15 0.019
Canon EOS 50D 22,3 × 14,9 0.019
Canon EOS M (*) 22,3 x 14,9 ¿?
Canon EOS Kiss Digital N/350D/REBEL XT 22,2 x 14,8 0.019
Canon EOS Kiss Digital X/400D/REBEL XTi 22,2 x 14,8 0.019
Canon EOS DIGITAL REBEL Xsi/450D/ Kiss X2 22,2 x 14,8 0.019
Canon EOS Kiss X3/EOS REBEL T1i /EOS 500D 22,3 x 14,9 0.019
Canon EOS Kiss X4/EOS REBEL T2i /EOS 550D 22,3 x 14,9 0.019
Canon EOS Kiss X5/EOS REBEL T3i /EOS 600D 22,3 x 14,9 0.019
Canon EOS Kiss X6i/EOS 650D/EOS REBEL T4i 22,3 x 14,9 0.019
Canon EOS DIGITAL REBEL XS/ 1000D/ KISS F 22,2 x 14,8 0.019
Canon EOS Kiss X50/EOS REBEL T3 /EOS 1100D 22,2 x 14,7 0.019
Nikon D3 36 × 23,9 0.030
Nikon D3S 36 x 23,9 0.030
Nikon D3X 35,9 x 24,0 0.030
Nikon D4 36,0 × 23,9 0.030
Nikon D40 23,7 x 15,7 0.020
Nikon D60 23,6 x 15,8 0.020
Nikon D80 23,6 × 15,8 0.020
Nikon D90 23,6 x 15,8 0.020
Nikon D200 23,6 x 15,8 0.020
Nikon D300 23,6 x 15,8 0.020
Nikon D300S 23,6 x 15,8 0.020
Nikon D600 35,9 x 24 ¿?
Nikon D700 36 x 23,9 0.030
Nikon D800 35,9 x 24 0.030
Nikon D5000 23,6 x 15,8 0.020
Nikon D5100 23,6 x 15,7 0.020
Nikon D5200 23,5 x 15,6 ¿?
Nikon D7000 23,6 x 15,7 0.020
Olympus E-1 ¿? 0.015
Olympus E-3 18 × 13,5 0.015
Olympus E-30 17,3 x 13 0.015
Olympus E-300 ¿? 0.015
Olympus E-330 17,3 x 13 0.015
Olympus E-400 17,3 x 13 0.015
Olympus E-410 18 × 13,5 0.015
Olympus E-420 17,3 x 13 0.015
Olympus E-450 18 × 13,5 0.015
Olympus E-500 ¿? 0.015
Olympus E-510 17,3 x 13 0.015
Olympus E-520 18 × 13,5 0.015
Olympus E-620 17,3 x 13 0.015
avatar
Fernandez Oscar November 12, 2013 12:24AM
Hi all,
 
All these formulas, calculations and experience is useless if the stack program does not have them in mind, so all these calculations I have agreed with Rik, the developer of the famous program Zerene Stacker stacking. Maybe I can fail in the nomenclature of the terms used in the formulas and even in some of the photographic knowledge bases on the other hand, I consider myself a true novice in the field because one is learning every day around a bit and what best is considered an inexperienced.
 
Moreover, thanks to computers and calculate formulas are applied in fast moments today is entirely feasible and will finish implementing it sooner or later, but these formulas I have outlined are a gateway for those who do not know or are not yet applying. They're not far from a secret, are widely used simple formulas, so anyone can apply them to your circumstances.
 
Pay attention to the two images attached. In the first you can see as I not take enough photographs and made ​​the bands appear unfocused. In the second you can see how the mistake has been corrected and the entire piece appears focused.
 
Failed to calculate the distance between each photo, appears bands or "slices" without focusing
http://www.foro-minerales.com/forum/files/apiladoh003628_error_641.jpg

Here the problem is corrected by giving a proper displacement between each photo of stack
http://www.foro-minerales.com/forum/files/apiladoh003628_ok_153.jpg


And since I put this mineral and that the photos were once only for testing, here attached picture made ​​with more quality 10x where you can see better the details of the "balls" of Cornellita.

Connellita
Mine Clara, Rankach valley, Oberwolfach, Wolfach, Black Forest, Baden-Württemberg, Germany.
FOV 0.93 mm. The white ball with the green arrow is of medium size and measures 35 microns (0.035 mm)
http://www.foro-minerales.com/forum/files/apiladoh003686pbola_167.jpg

Regards, Oscar.
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