Ballpen, first shot

Just bought that first macro lens? Post here to get helpful feedback and answers to any questions you might have.

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amml2000uk
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Ballpen, first shot

Post by amml2000uk »

After deciding to wait with the microscope I tried to see what I can do with my current equipment. I reversed a Nikon 35mm f2 on my nikon 18-200mm sitting on my D80 and took 3 photos of my ballpen and stacked them. All hand held so it was a bit shaky.

I know its not that amazing quality wise but I love the colors and I was honestly surprised by the magnification. Straight away I ordered a linear stage as I realized it's impossible to do this by hand...

On a side note, how do I figure out the magnification? I suppose it's 200/35 so around 6x magnification, but it seems more to me.

Adrian

Image

rjlittlefield
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Post by rjlittlefield »

The easiest way to measure scale is to take a picture of a mm ruler, using the same optics setup that you used for the real subject.

I agree with your calculation that reversing a 35 mm in front of 200 mm should give about 5.7X magnification, but that depends on the zoom being cranked clear out to 200 mm and set to infinity focus. Focusing closer will give you a bit more magnification, zooming shorter will give you less.

How did you know how long to draw the 1 mm scale bar? As drawn it indicates a field width of 4.8 mm, which with your 23.6 mm sensor width would imply about 4.9X magnification.

--Rik

amml2000uk
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Post by amml2000uk »

The taking a picture of a mm ruler method is what I used to draw the 1mm line in photoshop. (I actually read your post on it so I tried it straight away, workerd really well)

Thanks, for the calculation using pixels, now I understand how to calculate magnification from pixels. The only thing I don't understand is why this method works, I couldn't figure it out from the scale bar posts.

Adrian

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Post by rjlittlefield »

I am a great fan of getting scale by taking pictures of rulers. It is so much more reliable than calculations.

I'm not sure what method you're talking about when you write "don't understand why this method works". Can you show a calculation that doesn't make sense? Perhaps I can explain it.

--Rik

amml2000uk
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Post by amml2000uk »

The calculation that doesn't make sense is this one:

Total width of Image: 32.78
Width of 1mm scale: 6.87
Width of sensor: 23.6mm

6.87/32.78 = 0.2096 (1mm on image equals 20.9% of total width)

0.2096*23.6 = 4.946 (1mm cover 4.946mm on sensor)

23.6/4.946 = 4.771 (magnification)

I might have just answered my own question. Is 1:1 magnification if 23.6mm in real life are 23.6mm on my camera sensor?

Adrian
Last edited by amml2000uk on Tue May 18, 2010 12:18 pm, edited 2 times in total.

amml2000uk
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Post by amml2000uk »

In case somebody else ever struggles with magnification, here's a simple guide to magnification:

http://www.cs.mtu.edu/~shene/DigiCam/Us ... ation.html

What confused me was how one can calculate magnification based on sensor size when different sensors have different resolutions. Now that I got my head around the problem and realized I shouldnt try to connect the two it's actually quite simple and everything makes sense.

Thanks
Last edited by amml2000uk on Tue May 18, 2010 5:53 am, edited 1 time in total.

ChrisLilley
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Post by ChrisLilley »

amml2000uk wrote:The calculation that doesn't make sense is this one:
Total width of Image: 32.78
Width of 1mm scale: 6.87
Adrian
What units are those?

I thought the size of a D80 sensor was 3872 x 2592 pixels, and 23.6 x 15.8 mm.

amml2000uk
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Post by amml2000uk »

These where the units photoshop gave me when I measured the lengths, they definately arent pixels. The unit doesnt really matter though as they are cancelled out anyway in the calculation. The sensor width is 23.6mm which is also used in the calculation.

Adrian

ChrisLilley
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Post by ChrisLilley »

Ah okay maybe points or something based on some notional dpi setting. As you say the units cancel out here to give a dimensionless ration - I just wondered where the numbers came from.

I also wondered whether 32.78 was a typo for 38.72 if you were using centi-pixels or something :)

rjlittlefield
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Post by rjlittlefield »

Adrian, at first reading I was delighted to hear that you had stepped through the calculation to see how it works.

But then when I looked closer, I see there is still some confusion. Your calculation goes astray at the end.

Magnification is defined as size_on_sensor / size_on_subject.

As soon as you know that "1mm on the subject covers 4.946mm on sensor", you can compute the magnification in one more step: 4.946 / 1 = 4.946 .

The last additional calculation that you did, 23.6/4.946 = 4.771, happens to yield a number that is very similar, but it is not the magnification. (In fact it is the field width, as measured at the subject.)

Perhaps another example with different values will make the situation clear.

Suppose that you move farther back and take another picture, in which the 1mm scale appears as 3.278 Photoshop units. This is 0.1 of the image width (32.78 Photoshop units), so the size on sensor must be 0.1*23.6 = 2.36 mm. The magnification is now 2.36, less than before, which makes sense because you have moved back. But the final calculation in your sequence would now be 23.6/2.36 = 10, greater than before, and clearly not making sense as a magnification. (It does, however, make sense as the field width, 10 mm.)

As an aside, I will mention that calculating magnification and scale are examples of an area of mathematics called "ratio proportion problems".

They are very practical but also surprisingly difficult for many people.

As a result, they are widely discussed --- do a Google search on ratio proportion problems and see how many hits you get!

Far too many of the discussions neglect to mention that it becomes easier to keep things straight if you just carry along all the units and treat them like variables. As you say, most of the units will cancel out, and the ones that are left should be just the ones you need. If they are not, then you made some mistake in either setting up the calculation or carrying it out.

Carrying along the units and canceling them as if they were variables is called the "factor label method". You can Google search for that phrase and get quite a few good discussions.

I hope this is helpful.

Thanks for tracking down that link about camera magnification. Lots of good stuff covered there.

--Rik

amml2000uk
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Post by amml2000uk »

Thanks a lot for your explaination Rik! I can't believe I made such a huge mistake. Now I know why my calculation has been haunting me all day!

Thanks.

Adrian

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Post by rjlittlefield »

Let me tell you a story...

I teach the entry-level algebra class at the local university. Most of the class time goes into standard symbol manipulation mixed with spreadsheet calculations to check results and to handle problems that can't be solved by shoving the symbols around.

But of course I spend some time on applications as well. In fact we spend about a week on ratio proportion problems, with particular attention to factor label method.

At the end of the semester, I give an exam question that looks something like this:
Assume that a car gets 25 miles per gallon of gas. How many pounds of CO2 does the car produce for every 10 miles of travel? Be sure to justify your answer — show your calculations and give references to any sources that you use.
Virtually every student successfully goes to the web and retrieves the critical information that burning a gallon of gas produces about 20 pounds of CO2. From there, it is a simple calculation to get the required answer: 10 miles at 25 miles per gallon = 0.4 gallon; 0.4 gallon times 20 pounds CO2 per gallon = 8 pounds CO2.

Nonetheless, on average about 1 student in 4 completely scrambles the calculation, putting the wrong numbers on top or bottom, sometimes even including the same number two or more times. One semester I got answers ranging from 0.04 pounds up to 88 pounds.

As an educator, I find this saddening. It seems clear that something has gone horribly wrong in those students' early education, to the point that I can't fix 'em up in one class.

On the other hand, the bright side is that making such a "huge mistake" as you did is actually quite common, and you shouldn't beat yourself up for it. Just note what went wrong and try to figure out what to do differently next time.

Cheers!

--Rik

amml2000uk
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Post by amml2000uk »

Haha, I hope I am not one of those students! I have actually been intensively preparing for my statistics (simulation modelling) exam tomorrow so my mind has been somewhere other than magnification.

It must be frustrating having so many students giving the wrong answer to such a question at University level. Now I actually feel a bit embarassed! Believe me, I will never make this mistake again =)

You seem like a good and patient teacher, your students are lucky!

Thanks

Adrian
Last edited by amml2000uk on Wed May 19, 2010 3:29 am, edited 1 time in total.

rjlittlefield
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Post by rjlittlefield »

About the CO2 and similar "story" problems, what is perhaps most interesting is that there is essentially zero correlation between doing well in the abstract work and doing well in the story problems.

I get students who can correctly rearrange equations with great facility but blithely kill patients with 100X overdoses of painkiller, while other students romp through the story problems as if they were nothing but can scarcely figure out how to solve a linear equation if it has more parentheses than usual. A great puzzlement... :?

Good luck on your simulation modeling exam -- statistics of simulations is always an interesting topic.

--Rik

PaulFurman
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Post by PaulFurman »

Beautiful shot. It makes me wonder what you wrote/drew with that pen :-)

I just remember: [sensor width/photographed width]
Pixels don't matter.

Pixels do matter though, of course, but in talking about magnification for macro photo work, pixels just aren't used. Where it is used is scanning, and that's the same issue of magnification. But I never heard anyone say they took a photo of a bee at 4,000 ppi. That would be about 1:1 or 1x on a 12 megapixel 24mm wide sensor, which happens to be about an inch, so easy math: 4,000 pixels per inch. I believe good film scanners do about 7,000 ppi and your 5x shot at 12 megapixels would be 20,000 ppi!

It helps to have a rough idea like that of what the numbers should be. 1-inch wide sensor with 4,000 pixels across. Or 24mm wide sensor and a 24mm wide subject at 1x and about 5mm wide subject at 5x [5x5=25].

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