AMENDMENT NO. 3 TO RIGHTS AGREEMENT, AS AMENDED

Exhibit 4.1

EXECUTION COPY

AMENDMENT NO. 3

TO

RIGHTS AGREEMENT, AS AMENDED

THIS AMENDMENT NO. 3 (this “Amendment”) to the Rights Agreement dated as of August 27, 1997, as amended on June 22, 1998, January 3, 2003, and November 6, 2003 (as so amended, the “Rights Agreement”), between CYTYC CORPORATION, a Delaware corporation (the “Company”), and COMPUTERSHARE TRUST COMPANY, N.A. (successor to EquiServe Trust Company, N.A., which was a successor to BankBoston, N.A.), as rights agent (the “Rights Agent”), is entered into this 20^th day of May, 2007.

WHEREAS, the Company and the Rights Agent are currently parties to the Rights Agreement and, in accordance with Section 27 of the Rights Agreement, the Company and the Rights Agent desire to amend the Rights Agreement on the terms and conditions hereinafter set forth;

WHEREAS, the Company, Hologic, Inc., a Delaware corporation (“Hologic”), and Nor’easter Corp., a Delaware corporation and a wholly-owned subsidiary of Hologic (the “Merger Subsidiary”), have entered into an Agreement and Plan of Merger (the “Merger Agreement”) pursuant to which, among other things, the Company will merge with and into Merger Subsidiary with Merger Subsidiary being the surviving corporation and a wholly-owned subsidiary of Hologic (the “Merger”);

WHEREAS, on May 20, 2007 the Board of Directors of the Company resolved to amend the Rights Agreement to render it inapplicable to the Merger Agreement, the Merger and the other transactions specifically contemplated thereby and to provide that the Rights Agreement will expire immediately prior to the effective time of the Merger; and

WHEREAS, for purposes of this Amendment, capitalized terms not otherwise defined herein shall have the respective meanings set forth in the Rights Agreement, as amended by this Amendment.

NOW, THEREFORE, in consideration of the premises and the mutual agreements herein set forth, the parties hereby agree as follows:

1. Amendment to Section 1.

(a) Section 1(a) of the Rights Agreement is hereby amended by adding the following new paragraph to the end of Section 1(a):

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, neither Hologic, Merger Subsidiary, nor any of either such parties’ Affiliates or Associates shall be deemed to be an Acquiring Person solely by reason of: (i) the approval, execution or delivery of the Merger Agreement, including any amendment or supplement thereto; (ii) the announcement or

consummation of the Merger; or (iii) the consummation of any of the transactions specifically contemplated by the Merger Agreement, each upon the terms and subject to the conditions of the Merger Agreement.

(b) Section 1(d) of the Rights Agreement is hereby amended by adding the following sentence to the end of Section 1(d):

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, and provided that the Merger Agreement has not been terminated pursuant to its terms, the term “Adverse Person” shall not include Hologic, Merger Subsidiary or any of their Affiliates and Associates.”

(c) Section 1(e) of the Rights Agreement is hereby amended by adding the following sentence to the end of Section 1(e):

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, no Adverse Person Event shall be deemed to have occurred solely by reason of: (i) the approval, execution or delivery of the Merger Agreement, including any amendment or supplement thereto; (ii) the announcement or consummation of the Merger; or (iii) the consummation of the transactions specifically contemplated by the Merger Agreement, each upon the terms and subject to the conditions of the Merger Agreement.”

(d) Section 1(r) of the Rights Agreement is hereby amended by adding the following new paragraph to the end of Section 1(r):

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, no Distribution Date shall be deemed to have occurred solely by reason of: (i) the approval, execution or delivery of the Merger Agreement, including any amendment or supplement thereto; (ii) the announcement or consummation of the Merger; or (iii) the consummation of the transactions specifically contemplated by the Merger Agreement, each upon the terms and subject to the conditions of the Merger Agreement.”

(e) Section 1 of the Rights Agreement is hereby amended by inserting the following text after Section 1(r) but before Section 1(s):

“(r-1) “Effective Time” shall mean the date that the Merger becomes effective pursuant to the terms and conditions of the Merger Agreement.”

(f) Section 1 of the Rights Agreement is hereby amended by inserting the following text after section 1(y) but before Section 1(z):

“(y-1) “Merger” shall mean the merger of the Company with and into Merger Subsidiary pursuant to the terms and conditions of the Merger Agreement with Merger Subsidiary being the surviving corporation and a wholly-owned subsidiary of Hologic.”

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(y-2) “Merger Agreement” shall mean the Agreement and Plan of Merger by and among the Company, Hologic and Merger Subsidiary, dated as of May 20, 2007, which sets forth the terms and conditions of the Merger.

(y-3) “Merger Subsidiary” shall mean Nor’easter Corp., a wholly-owned subsidiary of Hologic and a Delaware corporation.

(y-4) “Hologic” shall mean Hologic, Inc., a Delaware corporation.

(g) Section 1(pp) of the Rights Agreement is hereby amended by adding the following new paragraph to the end of Section 1(pp):

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, no Stock Acquisition Date shall be deemed to have occurred solely by reason of: (i) the approval, execution or delivery of the Merger Agreement, including any amendment or supplement thereto; (ii) the announcement or consummation of the Merger; or (iii) the consummation of the transactions specifically contemplated thereby, each upon the terms and subject to the conditions of the Merger Agreement.”

(h) Section 1(uu) of the Rights Agreement is hereby amended by adding the following new paragraph to the end of Section 1(uu):

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, no Triggering Event shall be deemed to have occurred solely by reason of: (i) the approval, execution or delivery of the Merger Agreement, including any amendment or supplement thereto; (ii) the announcement or consummation of the Merger; or (iii) the consummation of the transactions specifically contemplated thereby, each upon the terms and subject to the conditions of the Merger Agreement.”

2. Amendment to Section 7(a). Section 7(a) of the Agreement is hereby amended by replacing the word “or” that appears immediately prior to the symbol “(iv)” with a comma, deleting the parenthetical contained at the end of Section 7(a) and by adding the following to the end of the amended Section 7(a):

“, or (v) the time immediately prior to the Effective Time (as defined in the Merger Agreement), whereupon the Rights shall expire (the earliest of (i), (ii), (iii), (iv) and (v) being therein referred to as the “Expiration Date”).

3. Amendment to Section 11(a)(ii). Section 11(a)(ii) of the Rights Agreement is amended by adding the following sentence at the end thereof:

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, none of the (i) approval, execution, delivery or performance of the Merger Agreement, (ii) the consummation of the Merger in accordance with the provisions of the Merger Agreement, (iii) the acquisition of the shares of

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Common Stock in accordance with the Merger Agreement pursuant to the Merger or (iv) the consummation of any other transaction to be effected pursuant to the Merger Agreement in accordance with the provisions of the Merger Agreement shall cause the Rights to be adjusted or become exercisable in accordance with this Section 11(a)(ii).”

4. Amendment to Section 13(d). Section 13(d) of the Rights Agreement is amended by adding the following sentence at the end thereof:

“Notwithstanding anything in this Agreement that might otherwise be deemed to the contrary, the provisions of this Section 13 shall not be applicable to the Merger.”

5. Effective Date. This Amendment shall become effective as of the date first above written.

6. Other Terms Unchanged. The Rights Agreement, as amended by this Amendment, shall remain and continue in full force and effect and is in all respects agreed to, ratified and confirmed hereby. Any reference to the Rights Agreement after the date first set forth above shall be deemed to be a reference to the Rights Agreement, as amended by this Amendment.

7. Benefits. Nothing in the Rights Agreement, as amended by this Amendment, shall be construed to give to any Person other than the Company, the Rights Agent and the registered holders of the Rights Certificates (and, prior to the Distribution Date, the registered holders of the Common Stock) any legal or equitable right, remedy or claim under the Rights Agreement, as amended by this Amendment; but the Rights Agreement, as amended by this Amendment, shall be for the sole and exclusive benefit of the Company, the Rights Agent and the registered holders of the Rights Certificates (and, prior to the Distribution Date, registered holders of the Common Stock).

8. Descriptive Headings. Descriptive headings of the several Sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

9. Governing Law. This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State.

10. Counterparts. This Amendment may be executed in any number of counterparts. It shall not be necessary that the signature of or on behalf of each party appears on each counterpart, but it shall be sufficient that the signature of or on behalf of each party appears on one or more of the counterparts. All counterparts shall collectively constitute a single agreement. It shall not be necessary in any proof of this Amendment to produce or account for more than a number of counterparts containing the respective signatures of or on behalf of all of the parties.

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11. Fax Transmission. A facsimile, telecopy or other reproduction of this Amendment may be executed by one or more parties hereto, and an executed copy of this Amendment may be delivered by one or more parties hereto by facsimile or similar instantaneous electronic transmission device pursuant to which the signature of or on behalf of such party can be seen, and such execution and delivery shall be considered valid, binding and effective for all purposes. At the request of any party hereto, all parties agree to execute an original of the Amendment as well as any facsimile, telecopy or other reproduction thereof.

12. Severability. If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

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