FIRST AMENDMENT TO

Exhibit 4.1

FIRST AMENDMENT TO

RIGHTS AGREEMENT

FIRST AMENDMENT, dated February 19, 2004 (the “Amendment”) to Rights Agreement dated as of June 2, 1998, between Credence Systems Corporation, a Delaware corporation (the “Company”) and Equiserve Trust Company, N.A. (formerly known as BankBoston, N.A.) as Rights Agent (the “Rights Agreement”). Capitalized terms used without definition herein are as defined in the Rights Agreement.

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

WHEREAS, 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 1. Section 1 shall be amended by deleting the definition of “Acquiring Person” in its entirety and replacing it with the following:

“Acquiring Person” shall mean any Person (as hereinafter defined) who or which, together with all Affiliates and Associates (as hereinafter defined) of such Person, shall be the Beneficial Owner (as hereinafter defined) of 15% or more of the shares of Common Stock of the Company then outstanding but shall not include (1) the Company, any Subsidiary (as such term is hereinafter defined) of the Company, any employee benefit plan of the Company or any Subsidiary of the Company, or any entity holding shares of Common Stock for or pursuant to the terms of any such plan, (2) any Person who was the Beneficial Owner (as hereinafter defined) of 15% or more of the shares of Common Stock outstanding as of the Close of Business (as hereinafter defined) on June 1, 1998 (a “Permitted Investor”), or any of its Affiliates or Associates (collectively with the Permitted Investor, an “Investor Group”) to the extent that the members of an Investor Group shall beneficially own in the aggregate up to, but not exceeding, the Special Threshold Percentage (as hereinafter defined) of the shares of Common Stock of the Company then outstanding or (3) any Person who acquires 15% or more of the shares of Common Stock of the Company then outstanding directly or indirectly from the Company in one or more transactions approved by a majority of the Board of Directors of the Company. Notwithstanding the foregoing:

(i) no Person shall become an “Acquiring Person” as the result of an acquisition of shares of Common Stock by the Company which, by reducing the number of shares outstanding, increases the proportionate number of shares beneficially owned by such Person to 15% or more of the shares of Common Stock of the Company then out standing; (or, in the case of an Investor Group, more than the Special Threshold Percentage of the shares of Common Stock of the Company then outstanding); provided, however, that if a Person shall become the Beneficial Owner of 15% or more of the shares of Common Stock of the Company then outstanding (or, in the case of an Investor

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Group, more than the Special Threshold Percentage of the shares of Common Stock of the Company then outstanding) by reason of share purchases by the Company and shall, after such share purchases by the Company, become the Beneficial Owner of any additional shares of Common Stock of the Company (or, in the case of the members of an Investor Group, become the Beneficial Owner of any additional shares of Common Stock of the Company), then such Person shall be deemed to be an “Acquiring Person” hereunder; and

(ii) if the Board of Directors of the Company determines in good faith that a Person who would otherwise be an “Acquiring Person” (as defined pursuant to the foregoing provisions of this definition), has become such inadvertently, and such Person divests as promptly as practicable a sufficient number of shares of Common Stock so that such Person would no longer be an “Acquiring Person” (as defined pursuant to the foregoing provisions of this definition), then such Person shall not be deemed to be an “Acquiring Person” for any purpose of this Agreement.”

2. Amendment to Section 21. Section 21 shall be amended by adding the following sentence after the end of the first sentence:

“In the event the transfer agency relationship in effect between the Company and the Rights Agent terminates, the Rights Agent will be deemed to resign automatically on the effective date of such termination; and any required notice will be sent by the Company.”

3. Amendment to add new Section 35. The Agreement shall be amended by adding the following entirely new Section 35 Force Majeure:

“Nothwithstanding anything to the contrary contained herein, Rights Agent shall not be liable for any delays or failures in performance resulting from acts beyond its reasonable control including, without limitation, acts of God, terrorist acts, shortage of supply, breakdowns or malfunctions, interruptions or malfunction of computer facilities, or loss of data due to power failures or mechanical difficulties with information storage or retrieval systems, labor difficulties, war, or civil unrest.”

4. Miscellaneous.

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

4.2. This 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.

4. 3. This Amendment and the Rights Agreement (including schedules and exhibits hereto and thereto) set forth the entire understanding of the parties relating to the subject matter hereof and thereof and supersede all prior agreements and

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understandings among or between any of the parties relating to the subject matter hereof. This 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.

4.4. 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 Amendment.

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