EXHIBIT 4.1

AMENDMENT NO. 1 TO RIGHTS AGREEMENT

This Amendment No. 1 (the “Amendment”) to the Rights Agreement dated as of April 17, 2008 between American Science and Engineering, Inc., a Massachusetts corporation, and American Stock Transfer & Trust Company, LLC, a New York corporation, as rights agent (the “Agreement”) is made and is effective as of December 18, 2014.  Capitalized terms used but not otherwise defined in this Amendment shall have the respective meanings accorded to them in the Agreement.

R E C I T A L S:

WHEREAS, the Company and Rights Agent have previously entered into the Agreement;

WHEREAS, no Distribution Date has occurred; and

WHEREAS, a majority of the Board has approved and authorized this Amendment pursuant to Section 27 of the Agreement

AGREEMENT

NOW, THEREFORE, in consideration of the premises and the mutual agreements herein set forth, the parties hereto hereby agree to amend the Agreement by:

1.   deleting the definition of Acquiring Person included in Section 1 and substituting in lieu thereof the following:

“Acquiring Person” shall mean any Person who or which, together with all Affiliates of such Person, shall be the Beneficial Owner of 15% or more of the shares of Common Stock then outstanding, but shall not include

(a)                                 the Company,

(b)                                 any Subsidiary of the Company,

(c)                                  any employee benefit plan of the Company or of any Subsidiary of the Company,

(d)                                 any Person organized, appointed, or established by the Company or a Subsidiary of the Company pursuant to the terms of any plan described in clause (c) above,

(e)                                  any Person who:

(i)                                     is entitled to report, and has reported or is required to report such ownership on Schedule 13G under the Exchange Act (or any comparable or successor report) or on Schedule 13D under the Exchange Act (or any comparable or successor report) which Schedule 13D does not state any intention to or reserve the right to control or influence the management or policies of the Company or engage in any of the actions specified in Item 4 of such Schedule (other than a disposition of the Common Stock) (a “13G Holder”) and,

(ii)                                  together with all Affiliates of such Person, is the Beneficial Owner of shares of Common Stock of the Company representing less than 20% of the shares of Common Stock of the Company then outstanding;

(iii)                               provided, however, that a Person who was deemed a 13G Holder shall no longer be deemed such if such Person files a statement on Schedule 13D pursuant to Rule 13d-1(a), 13d-1(e), 13d-1(f) or 13d-1(g) of the General Rules and Regulations under the Exchange Act, and shall be deemed an Acquiring Person if it is the Beneficial Owner of in excess of 14.9% of the Common Stock of the Company then outstanding at any point from the time it first files such a statement on Schedule 13D; further provided that if at the time of such filing such Person’s Beneficial Ownership is in excess of 14.9%, then such Person shall, if requested to do so by the Company, within a specified number of Business Days (to be specified by the Company, but in no case fewer than 10 Business Days) following such request from the Company to such Person, reduce its Beneficial Ownership (together with that of all Affiliates of such Person) to 14.9% or less of the Common Stock of the Company before being deemed an “Acquiring Person” but shall be deemed an “Acquiring Person” if after reducing its Beneficial Ownership to 14.9% or less it subsequently becomes the Beneficial Owner of in excess of 14.9% of the Common Stock of the Company or if, prior to reducing its Beneficial Ownership to 14.9% or less, it increases (or makes any offer or takes any other action that would increase) its Beneficial Ownership of the then-outstanding Common Stock of the Company, other than as a result of a repurchase of Common Stock by the Company or any Subsidiary of the Company, any employee benefit plan of the Company or of any Subsidiary of the Company, or any Person or entity organized, appointed or established by the Company for or pursuant to the terms of any such plan (any such repurchase being hereinafter referred to as a “Company Stock Buyback”), above the lowest Beneficial Ownership of such Person at any time during such 10-day period,

(f)                                   any Person who:

(i)                                     within 10 Business Days of being requested by the Company to advise it regarding the same, certifies to the Company that such Person acquired shares of Common Stock in excess of 14.9% inadvertently or without knowledge of the terms of the Rights; provided, however, that if the Person requested to so certify fails to do so within 10 Business Days, then such Person shall become an Acquiring Person immediately after such 10 Business Day period,

(ii)                                  together with all of such Person’s Affiliates, thereafter does not acquire additional shares of Common Stock while the Beneficial Owner of 15% or more of the shares of Common Stock then outstanding, and

(iii)                               if requested to do so by the Company, within a specified number of Business Days (to be specified by the Company, but in no case fewer than 10 Business Days) following such request from the Company to such Person, reduced its Beneficial Ownership of Common Stock to below 15% of the Common Stock then outstanding; provided, however, that if the Person requested to so reduce its Beneficial Ownership fails to do so within such specified number of Business Days, then such Person shall become an Acquiring Person immediately after such specified number of Business Days; or

(g)                                  any Person who becomes the Beneficial Owner of 15% or more of the shares of Common Stock then outstanding (20% in the case of a 13G Holder) solely as a result of a reduction in the number of shares of Common Stock outstanding due to a Company Stock Buyback, unless and until such Person, after becoming aware that such Person has become the Beneficial Owner of 15% or more of the then outstanding shares of Common Stock (20% in the case of a 13G Holder), increases (or makes any offer or takes any other action that would increase) its Beneficial Ownership of the then-outstanding Common Stock of the Company (other than as a result of a Company Stock Buyback); and

2.  deleting the definition of Offer Commencement Date in Section 1 and substituting in lieu thereof the following:

“Offer Commencement Date” shall mean the date of the commencement by any Acquiring Person, if upon consummation thereof such Person and Affiliates thereof would be the Beneficial Owner of 15% or more of the then outstanding shares of Common Stock (including any such date which is after the date of this Agreement and prior to the issuance of the Rights on the Dividend Record Date or thereafter); and

Except as amended hereby, the Agreement is hereby confirmed in all other respects.

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed and set their respective hands and seals, all as of the day and year first above written.