SECOND AMENDMENT TO

Exhibit 4.1

SECOND AMENDMENT TO

RIGHTS AGREEMENT

This SECOND AMENDMENT, dated as of August 27, 2004 (this “Second Amendment”) to the Rights Agreement (the “Rights Agreement”), dated as of June 2, 1998, by and between Credence Systems Corporation, a Delaware corporation (the “Company”) and Equiserve Trust Company, N.A. (formerly known as BankBoston, N.A.)(the “Rights Agent”), is entered into by and between the Company and the Rights Agent. Capitalized terms used without definition herein are as defined in the Rights Agreement.

WHEREAS, pursuant to the First Amendment to Rights Agreement, dated as of February 19, 2004, by and between the parties hereto (the “First Amendment”), the parties hereto amended the Rights Agreement to, among other things, replace the definition of “Acquiring Person” in accordance with Section 27 of the Rights Agreement; and

WHEREAS, the parties hereto now wish to amend the Rights Agreement in accordance with Section 27 of the Rights Agreement.

NOW, THEREFORE, in consideration of the mutual promises and covenants contained herein and for other good and valuable consideration the receipt and sufficiency of which the parties expressly acknowledge, the parties agree as follows.

1. Amendment to Section 7(a). Section 7(a) shall be amended by deleting Section 7(a) in its entirety and replacing it with the following:

(a) Except as provided in Sections 23(c) and 7(e), the registered holder of any Rights Certificate may exercise the Rights evidenced thereby (except as otherwise provided herein) in whole or in part at any time after the Distribution Date upon surrender of the Rights Certificate, with the form of election to purchase and certification on the reverse side thereof duly executed, to the Rights Agent at the office of the Rights Agent designated for such purpose, together with payment of the Purchase Price for each Unit of Preferred Stock as to which the Rights are exercised, at or prior to the earliest of (i) the Close of Business on August 31, 2004 (the “Final Expiration Date”), (ii) the time at which the Rights are redeemed as provided in Section 23 hereof (the “Redemption Date”), or (iii) the time at which such Rights are exchanged as provided in Section 24 hereof (the earlier of (i), (ii) and (iii) being the “Expiration Date”).

2. Miscellaneous.

2.1. The terms and provisions of the Rights Agreement shall remain in full force and effect except as specifically modified by the First Amendment and this Second Amendment.

2.2. This Second Amendment may be executed in one or more counterparts and delivered by facsimile, all of which shall be considered one and the

same agreement and shall become effective when one or more counterparts have been signed by each of the parties and delivered to the other parties, it being understood that all parties need not sign the same counterpart.

2.3. The First Amendment, this Second Amendment and the Rights Agreement (including schedules and exhibits hereto and thereto) sets forth the entire understanding of the parties relating to the subject matter hereof and thereof and supersede all prior agreements and understandings among or between any of the parties relating to the subject matter hereof. This Second Amendment may not be amended, modified, altered or supplemented other than by means of a written instrument duly executed and delivered on behalf of the parties hereto.

2.4. Each party shall execute and deliver such further documents and instruments and shall take such other further actions as may be required to carry out the intent and purposes of this Second Amendment.

[Signature Page to Follow]

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IN WITNESS WHEREOF, the undersigned have executed this Second Amendment as of the date first above written.

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