During prosecution, the Office issues first a non-final rejection, and then after the applicant is given an opportunity to amend, submit evidence, etc., a final rejection can be issued. If the applicant then intends to appeal the final rejection, they generally do not have the right to enter evidence (e.g., an expert declaration), amend the claims, etc. This is contrast to many foreign jurisdictions that commonly include amendments during an appeal proceeding.

Specifically referring to affidavits after final, MPEP 714.13 (citing to MPEP 1206) explains that entry after final is not a matter of right:

An affidavit or other evidence filed after a final rejection, but before or on the same date of filing an appeal, may be entered upon a showing of good and sufficient reasons why the affidavit or other evidence is necessary and was not earlier presented in compliance with 37 CFR 1.116 (e). See 37 CFR 41.33  and MPEP § 1206 for information on affidavit or other evidence filed after appeal.

MPEP 1206 explains that an affidavit or other evidence filed after the date of filing an appeal pursuant to § 41.31 (a)(1) through (a)(3) and prior to the date of filing a brief pursuant to § 41.37  may be admitted if the examiner determines that the affidavit or other evidence overcomes all rejections under appeal and that a showing of good and sufficient reasons why the affidavit or other evidence is necessary and was not earlier presented has been made.

So - you can see it is unlikely that you will convince an examiner to enter such evidence.

However, there are ways to present new evidence for the first time in an appeal, an example of which is illustrated in a recent case by Carnegie Melon University. Appeal 2023-001125, Application 16/516,664.

The invention at issue relates to to imaging systems and, more specifically, to an energy optimized imaging system that captures images using one or more directable beam light sources synchronized with one or more active pixel selectable photosensors. Claim 20 is reproduced below:

20. A method of detecting an image, comprising:
enabling a first row of a pixels of a two-dimensional pixel array to detect light reflected from at least one object illuminated by a first light pulse from a first scanning line of a directable light source, the first row of pixels in an epipolar configuration with the first scanning line; and
enabling a second row of pixels of a two-dimensional pixel array to detect light reflected from the at least one object illuminated by a second light pulse from a second scanning line of the directable light source, the second row of pixels in an epipolar configuration with the second scanning line.

An issue in this appeal was whether the provisional application supported the feature of the respective row of pixels in an epipolar configuration with the respective scanning line. If not, intervening prior art was applied to reject the claim. If so, the prior art was not available and there being no other rejections the claim would therefore presumably be allowable.

Without getting in to the details of what the privisional application did and did not describe, the provisional specification did refer to the term “epipolar” but did not refer to an “epipolar configuration” as such. To bolster the support in the specification, the applicant wanted to cite to evidence in a textbook to establish what one skilled in the art at the time of the invention would understand from the use of the term in the provisional specification. Specifically, the applicant argued as follows in their brief:

The term "epipolar" or "epipolar configuration" is a term of art well known by those of skill in the art. The Appellant has attached hereto, as a subject matter appendix in section VI, an excerpt from a textbook entitled "Multiple View Geometry in Computer Vision" (Hartley & Zisserman, ©2000, Cambridge University Press). This excerpt is provided both as proof that the phrase "epipolar configuration" is a term of art and for the benefit of the Board as an explanation of an epipolar configuration. Section 9.1 of this reference, provided in Section VI, explains epipolar geometry.

However, the applicant had not previously, before filing their appeal brief, ever referred to this evidence or submitted it to the Office. Nevertheless, the applicant was able to effectively use the evidence appendix of the appeal brief and include copies of the textbook, without objection from the examiner or board.

In the end the applicant was successful in its appeal. This case thus illustrates a useful way to have certain new evidence considered in an appeal even when never officially entered into the record. However, be careful, as pushing the limits so far as to attempt to circumvent explicit rules (such as in MPEP) is likely to cause your brief to be rejected as non-compliant.