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If i'm using a 24 megapixel camera and take two side-by-side images, then I combine the images in lightroom (using merge) to make a larger pano image, then shouldn't my image render a 48 megapixel file? I understand I'll loose a few megapixels for overlap.
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You should have a decent amount of overlap, so depending on how much you have will dictate the final file's size, but to have it nearly doubled isn't realistic.
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Not exactly, double size in pixels is not realistic as mentioned. Usually I am looking for 20% overlap or more for handheld shooting. When you shoot panorama using 9 images, for example, in three rows and columns, loss will be even greater of what you can expect.
Nothing wrong with your panorama, thats just how things works.
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in panoramic photography made from overlapping image series an overlap of 25% (1/4) to 33% (1/3) is ususl. 10% and less can work but leaves a very narrow space for finding matching image features (pattern recognition) and blending neighboured images seamlessly together. when stiching more than 2 images together avoid using more than 50% overlap as then the pattern recognition finds matching image features e.g. on image 1 and 3 and then (simplified) gets confused where to place the images. to quickly calculate the resulting pixel dimensions of a stitching result use a thumb rule: (n * image width * 0.66) + image width * 0.33 when using 33% overlap. if using portrait format this would mean for e.g. 5 images your 24MP cam: 5 * 2666 + 1 * 1333 pixel => 14665 pixel width and 6000 pixel height => ca. 88MP.
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Photoshop does not list the Megapixel (MP) value of an open image in it's interface (however it is listed in the Adobe Camera Raw interface). The following script can be used to quickly report on this value:
 
https://prepression.blogspot.com/2018/03/photoshop-mega-pixel-value-script-mp.html
https://github.com/MarshySwamp/Report-Megapixel-Value/blob/main/Report%20Megapixel%20Value.jsx