Exhibit 10.37

ELECTRO SCIENTIFIC INDUSTRIES, INC.

STOCK APPRECIATION RIGHTS AGREEMENT

This STOCK APPRECIATION RIGHTS AGREEMENT dated as of May 13, 2010, is between Electro Scientific Industries, Inc., an Oregon corporation (the “Company”), and Nicholas Konidaris (the “Recipient”), pursuant and subject to the Company’s 2004 Stock Incentive Plan (the “Plan”). The Company and the Recipient agree as follows:

1. SAR Grant. The Company hereby grants to the Recipient on the terms and conditions of this Agreement 65,000 stock appreciation rights (“SARs”). Upon exercise of a SAR in accordance with this Agreement, Recipient shall receive the number of shares of the Company’s Common Stock (“Common Stock”) equal to (i) the excess of the closing price of the Common Stock last reported before the time of exercise (the “Market Price”) over $        , (ii) multiplied by the number of SARs being surrendered, and (iii) dividing the result by the Market Price. No fractional shares shall be issued upon exercise of a SAR and in lieu thereof the Company will pay Recipient cash in an amount equal to the fraction. The terms and conditions of the SAR grant set forth in attached Exhibit A are incorporated into and made a part of this Agreement.

2. Grant Date. The Grant Date for this SAR is May 13, 2010. The SAR shall continue in effect until the date ten years after the Grant Date (the “Expiration Date”) unless earlier terminated as provided in Section 1.5 of Exhibit A or pursuant to the Plan.

3. Time of Exercise. Except as provided in Exhibit A or in the Plan, the SAR may be exercised from time to time in the following amounts:

25% on May 13, 2011

25% on May 13, 2012

25% on May 13, 2013

25% on May 13, 2014

If Recipient terminates his employment with the Company after Recipient attains age 67 with the intention of not seeking further full-time employment and prior to the final vesting date set forth in this Section 3, the SAR will continue to vest and be exercisable until the earlier of (i) the final vesting date set forth above and (ii) the third anniversary of the date of termination of employment.

(Signature Page Follows)

IN WITNESS WHEREOF, the parties have executed this Agreement as of the date written above.

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EXHIBIT A

SAR TERMS AND CONDITIONS

2004 Stock Incentive Plan

Pursuant to the Company’s 2004 Stock Incentive Plan (the “2004 Plan”), the Board of Directors has voted in favor of granting to the Recipient stock settled stock appreciation rights to receive Common Stock of the Company (the “SAR”) in the amount determined pursuant to the attached Agreement.

1. The SAR is granted upon the following terms:

1.1 Duration of SAR. Subject to reductions in the SAR period as hereinafter provided in the event of termination of employment or death of the Recipient, the SAR shall continue in effect for a period of 10 years from the Grant Date.

1.2 Time of Exercise. Except as provided in paragraphs 1.5 and 1.6 and the Plan (including Section 17 thereof), the SAR may be exercised as set forth in Section 3 of the Agreement.

1.3 Limitations on Rights to Exercise. Except as provided in paragraphs 1.5 and 1.6, Section 3 of the attached Agreement and the Employment Agreement, dated as of January 7, 2004, by and between the Company and Recipient, as amended, as the same may be amended, restated or modified from time to time, the SAR may not be exercised unless at the time of such exercise the Recipient is employed by the Company or any parent or subsidiary of the Company and shall have been so employed continuously since the date such SAR was granted.

1.4 Nonassignability. The SAR is nonassignable and nontransferable by the Recipient except by will or by the laws of descent and distribution of the state or country of the Recipient’s domicile at the time of death, and is exercisable during the Recipient’s lifetime only by the Recipient.

1.5 Termination of Employment.

(a) Unless otherwise determined by the Board of Directors, if a Recipient’s employment or service with the Company terminates for any reason other than in the circumstances specified in subsection (b) or (c) below or Section 1.6, his or her SAR may be exercised at any time before the expiration date of the SAR or the expiration of three months after the date of termination, whichever is the shorter period, but only if and to the extent the Recipient was entitled to exercise the SAR at the date of termination.

(b) Unless otherwise determined by the Board of Directors, if a Recipient’s employment or service with the Company terminates because of total disability, his or her SAR may be exercised at any time before the expiration date of the SAR or before the date 12 months after the date of termination, whichever is the shorter period, but only if and to the extent the Recipient was entitled to exercise the SAR at the date of termination. The term “total disability” means a medically determinable mental or physical impairment that is expected to result in death or has lasted or is expected to last for a continuous period of 12 months or more and that, in the opinion of the Company and two independent physicians approved by the Company, causes the Recipient to be unable to perform his or her duties as an employee, director, officer or consultant of the Company and unable to be engaged in any substantial gainful activity. Total disability shall be deemed to have occurred after both of the following have occurred:

(A) The two independent physicians have furnished their written opinion of total disability to the Company; and

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(B) The Company has reached an opinion of total disability.

(c) Unless otherwise determined by the Board of Directors, if a Recipient dies while employed by or providing service to the Company, his or her SAR may be exercised at any time before the expiration date of the SAR or before the date 12 months after the date of death, whichever is the shorter period, but only if and to the extent the Recipient was entitled to exercise the SAR at the date of death and only by the person or persons to whom the Recipient’s rights under the SAR shall pass by the Recipient’s will or by the laws of descent and distribution of the state or country of domicile at the time of death.

(d) To the extent the SAR held by any deceased Recipient or by the Recipient whose employment is terminated shall not have been exercised within the limited periods provided above, all further rights to receive shares pursuant to the SAR shall cease and terminate at the expiration of such periods.

(e) Absence on leave approved by the Company or on account of illness or disability shall not be deemed a termination or interruption of employment or service. Unless otherwise determined by the Board of Directors, vesting of SARs shall continue during a medical, family, military or other leave of absence, whether paid or unpaid.

1.6 Change in Control. Except as otherwise provided in the Employment Agreement:

(a) If as a result of a Change in Control, the Company’s Common Stock ceases to be listed for trading on a national securities exchange (an “Exchange”) and the voting securities of the resulting corporation or the acquiring corporation, as the case may be (including without limitation, the voting securities of any corporation which as a result of the Change in Control owns the Company or all or substantially all of the Company’s assets either directly or through one or more subsidiaries) (the “Surviving Company”), are traded on an Exchange, any SARs subject to this award that are unvested on the date of the Change in Control shall continue to vest according to the terms and conditions of this award and this award shall be replaced with an award for voting securities of the Surviving Corporation (a “Replacement Award”), which Replacement Award shall consist of SARs with the number of underlying shares and an exercise price determined in a manner consistent with Section 424(a) of the Internal Revenue Code of 1986, as amended, with vesting and any other terms continuing in the same manner as this award; provided, however, that in the event of a termination of Recipient’s employment by the Company or the Surviving Company without Cause or by the Recipient for Good Reason during the vesting period of any Replacement Award, the Replacement Award shall immediately vest; and provided further that upon the vesting date of all or a portion of a Replacement Award, the Company or the Surviving Company shall pay to Recipient a lump sum cash payment, paid as soon as practicable and in any event not later than March 15 of the calendar year following the calendar year of termination, equal to the decrease, if any, in the value of a share of the Surviving Company’s voting securities from the date of the Change in Control (as increased on a calendar quarterly basis using an annual interest rate, as of the last business day of the calendar quarter, for zero-coupon U.S. government securities with a constant maturity closest in length to the time period between the date of the Change in Control and the date of vesting of the Replacement Award) to the time of vesting multiplied by the total number of SARs vesting on such date.

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(b) If as a result of a Change in Control, the Company’s Common Stock continues to be listed for trading on an Exchange, any SARs that are unvested on the date of the Change of Control shall continue to vest according to the terms and conditions of this award; provided however, that, in the event of a termination of Recipient’s employment by the Company without Cause or by the Recipient for Good Reason during the vesting period of this award such award shall immediately vest; and provided further that upon the vesting date of all or portion of this award, the Company shall pay to Recipient an additional lump sum cash payment, paid as soon as practicable and in any event not later than March 15 of the calendar year following the calendar year of termination, equal to the decrease, if any, in the value of a share of the Company’s stock from the date of the Change in Control (as increased on a calendar quarterly basis using an annual interest rate, as of the last business day of the calendar quarter, for zero-coupon U.S. government securities with a constant maturity closest in length to the time period between the date of the Change in Control and the date of the vesting) to the time of vesting, multiplied by the total number of SARs vesting on such date.

(c) If (i) a change in ownership of the Company occurs (applying the definition of “change in the ownership of a corporation” set forth in Treasury Regulation Section 1.409A(3)(i)(5)(v), replacing “50 percent” with “75 percent”) or (ii) there is a change in the ownership of a substantial portion of the assets of the Company (applying the definition of “change in the ownership of a substantial portion of a corporation’s assets” set forth in Treasury Regulation Section 1.409A(3)(i)(5)(vii), replacing “40 percent” with “all or substantially all”), and the voting securities of the Surviving Company or the Company after the transaction are not listed on an Exchange, then all unvested SARs subject to this award shall vest immediately prior to the closing of such transaction.

(d) For purposes of this Agreement, a “Change in Control” of the Company shall mean the occurrence of any of the following events:

(A) any consolidation, merger or plan of share exchange involving the Company (a “Merger”) as a result of which the holders of outstanding securities of the Company ordinarily having the right to vote for the election of directors (“Voting Securities”) immediately prior to the Merger do not continue to hold at least 50% of the combined voting power of the outstanding Voting Securities of the surviving or continuing corporation immediately after the Merger, disregarding any Voting Securities issued or retained by such holders in respect of securities of any other party to the Merger;

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(B) any sale, lease, exchange or other transfer (in one transaction or a series of related transactions) of all, or substantially all, the assets of the Company;

(C) the adoption of any plan or proposal for the liquidation or dissolution of the Company;

(D) at any time during a period of two consecutive years, individuals who at the beginning of such period constituted the Board of Directors (“Incumbent Directors”) shall cease for any reason to constitute at least a majority thereof, unless each new director elected during such two-year period was nominated or elected by two-thirds of the Incumbent Directors then in office and voting (with new directors nominated or elected by two-thirds of the Incumbent Directors also being deemed to be Incumbent Directors); or

(E) any Person (as hereinafter defined) shall, as a result of a tender or exchange offer, open market purchases, or privately negotiated purchases from anyone other than the Company, have become the beneficial owner (within the meaning of Rule 13d-3 under the Securities Exchange Act of 1934), directly or indirectly, of Voting Securities representing fifty percent (50%) or more of the combined voting power of the then outstanding Voting Securities.

Notwithstanding anything in the foregoing to the contrary, unless otherwise determined by the Board of Directors, no Change in Control shall be deemed to have occurred for purposes of this Agreement if (1) the Recipient acquires (other than on the same basis as all other holders of the Company Common Stock) an equity interest in an entity that acquires the Company in a Change in Control otherwise described under subparagraph (A) or (B) above, or (2) the Recipient is part of group that constitutes a Person which becomes a beneficial owner of Voting Securities in a transaction that otherwise would have resulted in a Change in Control under subparagraph (E) above.

(e) For purposes of this Agreement, the term “Person” shall mean and include any individual, corporation, partnership, group, association or other “person”, as such term is used in Section 14 (d) of the Securities Exchange Act of 1934 (the “Exchange Act”), other than the Company, a wholly owned subsidiary of the Company or any employee benefit plan(s) sponsored by the Company.

(f) Cause. Termination by the Company of Recipient’s employment for “Cause” shall mean termination upon (A) the willful and continued failure by the Recipient to perform substantially the Recipient’s reasonably assigned duties with the Company consistent with those duties assigned to the Recipient prior to the Change in Control (other than any such failure resulting from the Recipient’s incapacity due to physical or mental illness) after a written demand for substantial performance is delivered to the Recipient by the Chairman of the Board of Directors or Chief Executive Officer of the Company or the Surviving Company or, if Recipient is not an officer, or an officer or manager with responsibility for Recipient’s department, which specifically identifies the manner in which such executive, officer or manager believes that the Recipient has not substantially performed the Recipient’s duties, (B) the conviction of guilty or entering of a nolo contendere plea to a felony which is materially and demonstrably injurious to the Company or the Surviving Company or (C) the commission of an act by Recipient, or the failure of Recipient to act, which constitutes gross negligence or gross misconduct. For purposes of this paragraph (e), no act, or failure to act, on the Recipient’s part shall be considered “willful” unless done, or omitted to be done, by the Recipient in knowing bad faith. Any act, or failure to act based upon authority given pursuant to a resolution duly adopted by the Board of Directors or based upon the advice of counsel for the Company or the Surviving Company shall be conclusively presumed to be done, or omitted to be done, by the Recipient in good faith.

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(g) Good Reason. Termination by the Recipient of his or her employment for “Good Reason” shall mean termination based on the following, after notice to the Company or the Surviving Company of the condition within one year of the occurrence of the condition and the failure of the Company or the Surviving Company to remedy the condition within 30 days after notice:

(A) a material diminution of Recipient’s status, title, position(s) or responsibilities from Recipient’s status, title, position(s) and responsibilities as in effect immediately prior to the Change in Control or the assignment to Recipient of any duties or responsibilities which are inconsistent with such status, title, position(s) or responsibilities (in either case other than isolated, insubstantial or inadvertent actions which are remedied after notice), or any removal of Recipient from such position(s), except in connection with the termination of Recipient’s employment for Cause, total disability (as defined in Section 1.5(b)) or as a result of Recipient’s death or voluntarily by Recipient other than for Good Reason;

(B) a material reduction by the Company or Surviving Company in Recipient’s rate of base salary, bonus or incentive opportunity or a material reduction in benefits (other than reductions that do not impact Recipient’s compensation opportunity, taken as a whole, or a reduction in benefits applicable to substantially all employees); or

(C) the Company’s or Surviving Company’s requiring Recipient to be based more than fifty miles from the principal office at in which Recipient is based immediately prior to the Change in Control, except for reasonably required travel on the Company’s business.

1.7 Method of Exercise. Shares may be acquired pursuant to the award only upon receipt by the Company of notice in writing from the Recipient of the Recipient’s intention to exercise, specifying the number of SARs as to which the Recipient desires to exercise the award and the date on which the Recipient desires to complete the transaction, which shall not be more than 30 days after receipt of the notice, and, unless in the opinion of counsel for the Company such a representation is not required in order to comply with the Securities Act of 1933, as amended, containing a representation that it is the Recipient’s present intention to acquire the shares for investment and not with a view to distribution. The Recipient shall have none of the rights of a shareholder until a certificate for shares is issued to the Recipient. No fractional shares shall be issued and in lieu thereof the Company shall pay Recipient cash equal to the value of such fractional share on the date of exercise. The Recipient shall, upon notification of the amount due, if any, and prior to or concurrently with delivery of the certificates representing the shares with respect to which the SAR was exercised, pay to the Company amounts necessary to satisfy any applicable federal, state and local withholding tax requirements. If additional withholding becomes required beyond any amount deposited before delivery of the certificates, the Recipient shall pay such amount to the Company on demand.

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1.8 Changes in Capital Structure. In the event that the outstanding shares of Common Stock of the Company are hereafter increased or decreased or changed into or exchanged for a different number or kind of shares or other securities of the Company or another corporation, by reason of any reorganization, merger, consolidation, recapitalization, reclassification, stock split-up, combination of shares, or dividend payable in shares, appropriate adjustment shall be made by the Board of Directors in the number of SARs subject to this Agreement and/or the amount payable on exercise of the SARs. Any such adjustment made by the Board of Directors shall be conclusive.

2. The obligations of the Company under this Agreement are subject to the approval of such state or federal authorities or agencies, if any, as may have jurisdiction in the matter. The Company will use its best efforts to take such steps as may be required by state or federal law or applicable regulations, including rules and regulations of the Securities and Exchange Commission and any stock exchange on which the Company’s shares may then be listed, in connection with the issuance or sale of any shares acquired upon the exercise of the SAR.

3. Nothing in the 2004 Plan or this Agreement shall confer upon the Recipient any right to be continued in the employment of the Company or any subsidiary of the Company, or to interfere in any way with the right of the Company or any subsidiary by whom the Recipient is employed to terminate the Recipient’s employment at any time, with or without cause.

4. This Agreement shall be binding upon and shall inure to the benefit of any successor or successors of the Company but except as hereinabove provided the SAR herein granted shall not be assigned or otherwise disposed of by the Recipient.

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