If the pattern you design for a photomask is not "mirror-symmetric" it will appear as a normal image from one side of the mask and a mirror-image from the other side. This is called Mask Parity. The fundamental question we have when we build a mask is "Which pattern orientation do you want us to write on the chrome surface of the mask: the image you supplied or the mirror-image?"
Answering this question can get confusing since the mask supplier and the mask designer often have different perspectives of the mask: Masks are written chrome-up but are commonly used chrome-down. What is mirrored from one side is not mirrored from the other.
To clarify, we borrow terminology from photography called Right-Reading and Wrong-Reading. In photography, the original image is defined as Right-Reading and the mirror of the original image is called Wrong-Reading.
In photolithography, we define the original design pattern you supply (whatever that may be) as Right-Reading and the mirror image of the design pattern as Wrong-Reading.
Having text on the mask can be another point of confusion. When we refer to text on a mask as right-reading and wrong-reading, what we are referring to is normal text and mirrored text. So a right-reading image, as illustrated here, can have wrong-reading text. The key point is that image parity is not defined by text parity.
To tell us the mask parity you want, we need to know both the image parity (right-reading or wrong-reading) and the frame of reference (chrome-up or chrome-down).
Even though we are showing four possible combinations in this matrix, note that there are only two states of parity since Right-Reading Chrome-Up is the same physical mask as Wrong-Reading Chrome-Down and Wrong-Reading Chrome-Up is the same physical mask as Right-Reading Chrome-Down.