Jacek,
I have a glass micrometer, so just. Thank you
If you have a stage micrometer (calibrated glass measurement slide) it is easy to calibrate your system. Then you can measure subject size from a picture or also create "scale bars". It takes a little time initially to do the needed measurements, but you only need to do it one time (unless you change your setup!) I'll go over a way of doing this. It really is not difficult or complicated, but with the language difference I hope it is not too confusing.
(The rest of this message is only accurate if you photograph in the same manner all of the time. That means using the
same eyepiece with the camera. And also using the camera at the
same focal length setting, the
same lens focus distance setting, and the
same pixel dimensions for all your pictures.
Each pixel in your Lumix DMC-TZ8 camera measures 1.4 micron.
With this camera you can choose and set a wide variety of picture pixel "resolutions" on the camera... such as 4000x3000 (4:3 ratio) or 4176 x 2784 (3:2 ratio) ... so you need to know what is set in the camera. You most likely are using 4000x3000 pixels. (I'll use 4000x3000 for the rest of this example). At 4000 pixels wide, and each pixel being 1.4 micron, it means you are using an actual x-dimension of 5.6mm on the camera sensor.
All you really need to do is photograph a part of the calibrated glass stage micrometer, and determine how many pixels long that measurement is in the picture.
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Example (I'll just make up reasonable numbers for this example, I don't know what your actual numbers would be):
Many stage micrometers (the calibrated glass measurement slide) are calibrated in 10 micron increments. For this example let us say that you take a photograph of this scale using a 10X objective. In Photoshop (or another program) you measure the number of pixels that make up the distance covered by 10 increments on the slide. On the subject slide this is exactly 10X10 micron =100 micron. Let us say that in Photoshop you measure 221 pixels along that 100 micro subject size. Now you know that when you use your 10X objective, 1 micron in subject size will measure 2.2 pixels in the image (221 pixel/100micron). Write that down! ...
2.2pixel/micron with 10X. You can now measure any "x" or "y" distance in any picture taken with the 10X by simply measuring its length in pixels and dividing it by 2.2. (Remember! You need to use your own actual measurements. I made these numbers up for this example).
The most accurate thing to do next is to measure like this for each different objective you use, and determine a "pixel/micron" value for each. (And for best accuracy use a measurement that goes nearly the full width of the picture). But if you don't need to be super accurate (or are a little lazy like me

) you can determine the magnification change provided by the combination of the eyepiece + camera used. If you don't change camera and eyepiece settings, the magnification factor they provide remains constant with all objectives. Generally I have found that the marked power of objectives is pretty accurate.
But again... it is always "best" to measure each objective individually. In the example above, a 100 micron subject measured 221 pixels on the sensor. Since each pixel is 1.4 micron, that means that the 100 micron subject was recorded at a size of 310 micron on the sensor (221 x 1.4 micron). That means with a 10X objective, the camera + eyepiece gives you a magnification factor of 310/100 = 3.1X. If you keep the camera at the same settings, you can apply that magnification factor value to other objectives. That would mean that using the numbers in this example:
A 1X objective would records a image at 0.31X on sensor. (1.1 pixels/micron)
A 10X objective records an image at 3.1X on sensor. (2.2 pixels/micron)
A 20X objective would record an image at 6.2X on sensor (4.4pixels/micron)
A 40 X objective would record an image at 12.4X on sensor (8.9 pixels/micron)
A 60 X objective would record an image at 18.6X on sensor (13.3 pixels/micron)
a 100X objective would record an image at 31X on sensor. (22 pixels/micron)
Be sure to plug in your own measured values in the example given. For your particular camera, the Lumix DMC-TZ8, you should use 1.4 micron for the pixel dimension. I used a picture dimension of 4000 pixels wide. I believe that is the "default" for your camera, but there are quite a few pixel resolutions that can be set, so be sure you use the value for the picture size you are using. And remember that it is best to use the same focal length and focus setting on the camera. Otherwise you really would need to photograph and measure your calibrated slide every time
