SETTLEMENT AGREEMENT

Exhibit 10.3

Execution Version

SETTLEMENT AGREEMENT

This Settlement Agreement (this “Agreement”) is made and entered into as of December 7, 2009, by and among Analogic Corporation (the “Company” or “Analogic”) and the entities and natural persons listed on Exhibit A hereto (collectively, the “Ramius Group”) (each of the Company and the Ramius Group, a “Party” to this Agreement, and collectively, the “Parties”).

RECITALS:

WHEREAS, the Company and the Ramius Group have engaged in various discussions and communications concerning the Company’s business, financial performance and strategic plans; and

WHEREAS, the Ramius Group duly submitted a nomination letter to the Company on October 28, 2009 (the “Nomination Letter”) nominating three (3) individuals as director candidates for election to the Company’s board of directors (the “Board”) at the 2010 annual meeting of stockholders of the Company (including any adjournment or postponement thereof, the “2010 Annual Meeting”); and

WHEREAS, the Ramius Group has reviewed and approved the statement for inclusion in the Company’s First Quarter Fiscal Year 2010 Earnings Release outlining the primary pathways through which the Company intends to reach its objective of achieving double digit operating margins by Fiscal Year 2012 (the “Financial Pathway Statement”); and

WHEREAS, the Company included the Financial Pathway Statement in the form approved by the Ramius Group in its First Quarter Fiscal Year 2010 Earnings Release; and

WHEREAS, the Company and the members of the Ramius Group have determined (i) that the interests of the Company and its stockholders would be best served at this time by, among other things, avoiding an election contest and the expense and disruption that may result therefrom and (ii) to come to an agreement with respect to the composition of the Board, certain matters related to the 2010 Annual Meeting and certain other matters, as provided in this Agreement.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants and agreements contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto, intending to be legally bound hereby, agree as follows:

1. Board Matters; Board Appointment; 2010 Annual Meeting; Committee Appointment; Independent Candidate Appointment.

(a) The Company agrees to nominate Burton P. Drayer, M.D. to be elected as a member of the Board at the 2010 Annual Meeting to serve for a term of one year expiring at the 2011 annual meeting of stockholders of the Company (including any adjournment or postponement thereof, the “2011 Annual Meeting”) and will recommend a vote “for” Dr. Drayer at the 2010 Annual Meeting and solicit proxies from all stockholders to vote all shares of Common Stock in favor of the election to the Board of Dr. Drayer. At the 2010 Annual Meeting, the Ramius Group shall appear in person or by proxy and vote all shares of Common Stock

beneficially owned by it and its affiliates in favor of the election to the Board of the Company’s slate of nominees (the “2010 Nominees”). The Ramius Group shall cause to be executed proxies for the 2010 Nominees (in the form utilized by the Company to solicit proxies for all stockholders) so as to vote all shares of Common Stock beneficially owned by it and its affiliates in favor of the election to the Board of the 2010 Nominees. The Ramius Group shall not withdraw or modify any such proxies.

(b) Upon the conclusion of the 2010 Annual Meeting, the Company shall take all action necessary in furtherance of the appointment of Dr. Drayer to the Nominating and Corporate Governance Committee of the Company (the “Nominating Committee”).

(c) Upon execution of this Agreement, the Ramius Group hereby withdraws its Nomination Letter.

(d) The Company agrees that it will hold the 2010 Annual Meeting no later than January 31, 2010.

(e) If Dr. Drayer leaves the Board (whether by resignation or otherwise) before the conclusion of the 2011 Annual Meeting, the Ramius Group will be entitled to recommend to the Nominating Committee replacement director(s) provided that such replacement director(s) qualify as “independent” pursuant to NASDAQ listing standards. The Nominating Committee will not unreasonably withhold acceptance of any replacement director recommended by the Ramius Group. In the event the Nominating Committee does not accept a replacement director recommended by the Ramius Group, the Ramius Group will have the right to recommend additional replacement director(s) for consideration by the Nominating Committee. The Company will cause the Board to appoint such replacement director(s) to the Board and the Nominating Committee no later than fifteen (15) business days after the Nominating Committee’s recommendation of such replacement director(s).

(f) Except as set forth in Section 2(e)(ii), the parties hereto acknowledge that the only matters that may be presented by the Company for consideration at the 2010 Annual Meeting include (i) the election of the 2010 Nominees, (ii) the approval of the Company’s 2009 Stock Incentive Plan, and (iii) the ratification of the Company’s independent registered public accounting firm.

(g) Neither the Ramius Group nor any member of the Ramius Group shall (i) nominate any person for election at the 2010 Annual Meeting or (ii) submit any proposal for consideration at, or bring any other business before, the 2010 Annual Meeting, directly or indirectly. The Ramius Group shall not enter into any agreement, understanding or arrangement with the purpose or effect to cause or further any of the foregoing or otherwise engage in any activities with the purpose or effect to cause or further any of the foregoing.

2. Independent Candidate Search; Appointment of Independent Candidate.

(a) Upon the execution of this Agreement, the Nominating Committee will undertake a process to identify potential independent candidates (the “Independent Candidates”) from which the Board will select one Independent Candidate to appoint as a member of the Board by no later than March 31, 2010 (the “New Director).

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(b) The Company will advise the Ramius Group of the desired qualifications for the Independent Candidates. The Ramius Group will be permitted to submit Independent Candidate(s) (the “Ramius Candidates”) for consideration by the Nominating Committee.

(c) The Company will provide the Ramius Group with a list of the Independent Candidates being considered by the Nominating Committee no later than February 15, 2010. The Ramius Group will be permitted to meet with (telephonically or otherwise) and review the qualifications of the Independent Candidates and provide the Nominating Committee with its feedback on those candidates.

(d) Any vote by the Nominating Committee to recommend an Independent Candidate, who is not a Ramius Candidate, for appointment as the New Director shall be unanimous.

(e) In order to accommodate the appointment of the New Director to the Board, the Board shall either (i) secure the resignation of an existing director prior to the time the Company mails its definitive proxy materials in connection with the 2010 Annual Meeting (with such resignation to be tendered and effective on or before March 31, 2010); or (ii) put up for stockholder vote at the 2010 Annual Meeting a proposal to amend the Company’s Bylaws to change the variable range for the size of the Board from “not less than five, nor more than ten” members to “not less than five, nor more than eleven” members. (the “Bylaw Amendment”)

(f) The Company agrees that the Board shall only be increased at any time prior to the conclusion of the 2011 Annual Meeting in connection with the appointment of the New Director. In the event that the Company increases the size of the Board to eleven (11) members to accommodate the appointment of the New Director and a vacancy thereafter exists on the Board at any time prior to the conclusion of the 2011 Annual Meeting, other than a vacancy resulting from Dr. Drayer or the New Director leaving the Board, the Company agrees not to fill such vacancy and to reduce the size of the Board to ten (10) members.

(g) If the New Director leaves the Board (whether by resignation or otherwise) before the conclusion of the 2011 Annual Meeting, a replacement director will be identified and appointed to the Board in a process consistent with this Section 2.

(h) In the event that the Company elects to comply with Section 2(e)(ii) above, the Company will recommend a vote “for” the Bylaw Amendment at the 2010 Annual Meeting and solicit proxies from all stockholders to vote all shares of Common Stock in favor of such proposal.

3. Representations and Warranties of the Company.

The Company represents and warrants to the Ramius Group that (a) the Company has the corporate power and authority to execute this Agreement and to bind it thereto, (b) this Agreement has been duly and validly authorized, executed and delivered by the Company, constitutes a valid and binding obligation and agreement of the Company, and is enforceable against the Company in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles

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and (c) the execution, delivery and performance of this Agreement by the Company does not and will not violate or conflict with (i) any law, rule, regulation, order, judgment or decree applicable to it, or (ii) result in any breach or violation of or constitute a default (or an event which with notice or lapse of time or both could become a default) under or pursuant to, or result in the loss of a material benefit under, or give any right of termination, amendment, acceleration or cancellation of, any organizational document, agreement, contract, commitment, understanding or arrangement to which the Company is a party or by which it is bound.

4. Representations and Warranties of the Ramius Group.

The Ramius Group shall cause its affiliates to comply with the terms of this Agreement. The Ramius Group represents and warrants to the Company that (a) the authorized signatory of the Ramius Group set forth on the signature page hereto has the power and authority to execute this Agreement and to bind it thereto this Agreement (b) this Agreement has been duly authorized, executed and delivered by the Ramius Group, and constitutes a valid and binding obligation of the Ramius Group, enforceable against the Ramius Group in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles, (c) the execution of this Agreement, the consummation of any of the transactions contemplated hereby, and the fulfillment of the terms hereof, in each case in accordance with the terms hereof, will not conflict with, or result in a breach or violation of the organizational documents of the Ramius Group as currently in effect and (d) the execution, delivery and performance of this Agreement by each member of the Ramius Group does not and will not violate or conflict with (i) any law, rule, regulation, order, judgment or decree applicable to it, or (ii) result in any breach or violation of or constitute a default (or an event which with notice or lapse of time or both could become a default) under or pursuant to, or result in the loss of a material benefit under, or give any right of termination, amendment, acceleration or cancellation of, any organizational document, agreement, contract, commitment, understanding or arrangement to which such member is a party or by which it is bound.

5. Press Release.

Promptly following the execution of this Agreement, the Company and the Ramius Group shall jointly issue a mutually agreeable press release (the “Mutual Press Release”) announcing the terms of this Agreement, substantially in the form attached hereto as Exhibit B. Prior to the issuance of the Mutual Press Release, neither the Company nor the Ramius Group shall issue any press release or public announcement regarding this Agreement or take any action that would require public disclosure thereof without the prior written consent of the other party.

6. Specific Performance.

Each of the members of the Ramius Group, on the one hand, and the Company, on the other hand, acknowledges and agrees that irreparable injury to the other party hereto would occur in the event any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached and that such injury would not be adequately compensable in damages. It is accordingly agreed that the members of the Ramius Group or any of them, on the one hand, and the Company, on the other hand (the “Moving Party”), shall each

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be entitled to specific enforcement of, and injunctive relief to prevent any violation of, the terms hereof, and the other party hereto will not take action, directly or indirectly, in opposition to the Moving Party seeking such relief on the grounds that any other remedy or relief is available at law or in equity.

7. Expenses.

The Company shall reimburse the Ramius Group for its reasonable, documented out-of-pocket fees and expenses (including legal expenses) incurred in connection with the matters related to the 2010 Annual Meeting and the negotiation and execution of this Agreement, provided that such reimbursement shall not exceed $35,000 in the aggregate.

8. Severability.

If any term, provision, covenant or restriction of this Agreement is held by a court of competent jurisdiction to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Agreement shall remain in full force and effect and shall in no way be affected, impaired or invalidated. It is hereby stipulated and declared to be the intention of the parties that the parties would have executed the remaining terms, provisions, covenants and restrictions without including any of such which may be hereafter declared invalid, void or unenforceable. In addition, the parties agree to use their best efforts to agree upon and substitute a valid and enforceable term, provision, covenant or restriction for any of such that is held invalid, void or enforceable by a court of competent jurisdiction.

9. Notices.

Any notices, consents, determinations, waivers or other communications required or permitted to be given under the terms of this Agreement must be in writing and will be deemed to have been delivered: (i) upon receipt, when delivered personally; (ii) upon receipt, when sent by facsimile (provided confirmation of transmission is mechanically or electronically generated and kept on file by the sending party); or (iii) one (1) business day after deposit with a nationally recognized overnight delivery service, in each case properly addressed to the party to receive the same. The addresses and facsimile numbers for such communications shall be:

If to the Company:

Analogic Corporation

8 Centennial Drive

Peabody, Massachusetts 01960

Attention: John J. Fry, General Counsel

Facsimile:

With a copy to:

WilmerHale

60 State Street

Boston, Massachusetts 02109

Attention: Michael J. LaCascia, Esq.

      Patrick J. Rondeau, Esq.

Facsimile: (617)  ###-###-####

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If to the Ramius Group or any member of the Ramius Group:

Ramius Value and Opportunity Master Fund Ltd

c/o RCG Starboard Advisors, LLC

599 Lexington Avenue, 20^th Floor

New York, New York 10022

Attention: Jeffrey C. Smith

      Owen S. Littman

Telephone: (212)  ###-###-####

Facsimile: (212)  ###-###-####

With a copy to:

Olshan Grundman Frome Rosenzweig & Wolosky LLP

Park Avenue Tower

65 East 55th Street

New York, New York 10022

Attention: Steven Wolosky, Esq.

Facsimile: (212)  ###-###-####

10. Applicable Law.

This Agreement shall be governed by, and interpreted in accordance with, the laws of the State of New York without regard to the principles of conflict of laws. Each of the Parties consents to the exclusive jurisdiction of the Federal and State courts of the State of New York for the decision of any disputes relating to this Agreement, and each agrees not to assert by way of motion, as a defense or otherwise, in any such suit, action or proceeding, any claim that such Party is not personally subject to the jurisdiction of such court, that the suit, action, or proceeding is brought in an inconvenient forum, that the venue of the suit, action or proceeding is improper, or that this Agreement may not be litigated in or by such court.

11. Counterparts.

This Agreement may be executed in one or more counterparts which together shall constitute a single agreement.

12. Entire Agreement; Amendment and Waiver; Successors and Assigns.

This Agreement contains the entire understanding of the parties hereto with respect to its subject matter. There are no restrictions, agreements, promises, representations, warranties, covenants or undertakings between the parties other than those expressly set forth herein. No modifications of this Agreement can be made except in writing signed by an authorized representative of each the Company and the Ramius Group. No failure on the part of any party to exercise, and no delay in exercising, any right, power or remedy hereunder shall operate as a waiver thereof, nor shall any single or partial exercise of such right, power or remedy by such party preclude any other or further exercise thereof or the exercise of any other right, power or

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remedy. All remedies hereunder are cumulative and are not exclusive of any other remedies provided by law. The terms and conditions of this Agreement shall be binding upon, inure to the benefit of, and be enforceable by the parties hereto and their respective successors, heirs, executors, legal representatives, and permitted assigns. No party shall assign this Agreement or any rights or obligations hereunder without, with respect to any member of the Ramius Group, the prior written consent of the Company, and with respect to the Company, the prior written consent of the Ramius Group.

13. Mutual Non-Disparagement.

For a period beginning on the effective date of this Agreement and ending on (i) the date that is one-month prior the nomination deadline for the 2011 Annual Meeting (in the event that the Company has appointed an Independent Candidate by March 31, 2010); or (ii) April 1, 2010 (in the event that the Company has failed to appoint an Independent Candidate by March 31, 2010), each of the Parties covenants and agrees that none of it or its respective subsidiaries, affiliates, successors, assigns, officers, key employees or directors shall in any way disparage, attempt to discredit, or otherwise call into disrepute, the other Parties or such other Parties’ subsidiaries, affiliates, successors, assigns, officers (including any current officer of a Party or a Parties’ subsidiaries who no longer serves in such capacity following the execution of this Agreement), directors (including any current director of a Party or a Parties’ subsidiaries who no longer serves in such capacity following the execution of this Agreement), employees, stockholders, agents, attorneys or representatives, or any of their products or services, in any manner that would damage the business or reputation of such other Parties, their products or services or their subsidiaries, affiliates, successors, assigns, officers (or former officers), directors (or former directors), employees, stockholders, agents, attorneys or representatives.

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IN WITNESS WHEREOF, this Agreement has been duly executed and delivered by the duly authorized signatories of the Parties as of the date hereof.

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EXHIBIT A

The Ramius Group

RAMIUS VALUE AND OPPORTUNITY MASTER FUND LTD

RCG PB, LTD

RAMIUS ENTERPRISE MASTER FUND LTD

RAMIUS ADVISORS, LLC

RCG STARBOARD ADVISORS, LLC

RAMIUS LLC

COWEN GROUP, INC.

RCG HOLDINGS LLC

C4S & CO., L.L.C.

PETER A. COHEN

MORGAN B. STARK

THOMAS W. STRAUSS

JEFFREY M. SOLOMON

BURTON P. DRAYER, M.D.

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EXHIBIT B

[MUTUAL PRESS RELEASE]

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NOT FOR IMMEDIATE WORLDWIDE RELEASE

For Further Information, Contact:

ANALOGIC ANNOUNCES SETTLEMENT AGREEMENT WITH RAMIUS

Will Nominate Dr. Burton Drayer to Serve on Analogic Board of Directors

Will Appoint Additional New Independent Director

Issues “Financial Pathway Statement” Outlining Strategy for Achieving Double-Digit Operating Margins

PEABODY, Mass. – December 9, 2009 – Analogic Corporation (NASDAQ: ALOG), a leading designer and manufacturer of medical imaging and aviation security technology, today announced that it has reached an agreement with Ramius Value and Opportunity Master Fund Ltd, an affiliate of RCG Starboard Advisors, LLC and Ramius LLC (collectively, “Ramius”), relating to the Company’s 2010 Annual Meeting of Stockholders. Ramius beneficially owns approximately 4.9% of Analogic’s outstanding shares. The Analogic 2010 Annual Meeting will be held on January 29, 2010 at the Company’s world headquarters in Peabody, Massachusetts.

Analogic will nominate Dr. Burton Drayer, Executive Vice President for Risk at The Mount Sinai Medical Center and Chairman and Director of Mount Sinai’s Department of Radiology, to stand for election as a new independent director on the Analogic Board at the January 2010 Annual Meeting. Dr. Drayer, who was recommended by Ramius, will fill the vacancy resulting from the previously announced departure of Analogic founder and Chairman Emeritus from the Company’s Board. It is expected that Dr. Drayer will also serve on the Nominating and Corporate Governance Committee.

Also at the 2010 Annual Meeting, Analogic will ask the Company’s shareholders to approve an increase of the size of the Analogic Board from ten to eleven members. Subject to shareholder approval, Analogic will appoint a new independent director to its Board by March 31, 2010. The Nominating Committee of Analogic’s Board will identify potential director candidates, including any proposed by Ramius and other Analogic stockholders, from which the Board will select one individual to appoint to the Board.

As part of the settlement agreement, Analogic also agreed to issue a “Financial Pathway Statement” in its earnings release for the First Quarter ended October 31, 2009. The statement outlines Analogic’s strategy for driving

enhanced profitability in each of the next three years, through organic measures within the Company’s control, on its pathway to double-digit operating margins by fiscal year 2012.

Ramius has withdrawn its nomination of director candidates to Analogic’s Board and has agreed to vote its shares in favor of each of the Board’s nominees.

“We welcome open dialogue with and input from our stockholders and are pleased to have reached this agreement with Ramius, which we believe serves the best interests of all Analogic stockholders,” said Jim Green, President and Chief Executive Officer of Analogic. “Our Board and management team are committed to continuing to work on behalf of all Analogic stockholders with the shared goal of enhancing value.”

“We are delighted to nominate Dr. Drayer for election to Analogic’s Board,” said Ed Voboril, Analogic Chairman of the Board of Directors. “Burt brings to Analogic significant industry experience due to his roles as a practitioner, professor, and business executive. As an Executive Vice President at Mount Sinai, he understands the economics of the health care industry. In addition, as a member of the faculty at the Mount Sinai School of Medicine and the President-elect of the Radiological Society of America, Burt is directly involved in education, research and health care policy. We strongly believe that Burt’s experience, coupled with his deep understanding of Analogic’s businesses, will be beneficial to the Company and all Analogic stockholders.”

On behalf of Ramius, Mark Mitchell said, “We are pleased to have worked constructively with Analogic with the shared goal of enhancing stockholder value. We support the Company’s commitment and strategy to significantly improve profitability in each of the next three years with the goal of achieving double digit operating margins by fiscal year 2012. We are confident that the nomination of Dr. Drayer to the Board and the Board’s commitment to adding another highly-qualified, independent director by March 31, 2010 will serve the best interests of Analogic and its stockholders.”

The complete Agreement will be included as an exhibit to the Company’s Current Report on Form 8-K to be filed with the Securities and Exchange Commission.

Burton Drayer, MD

Dr. Drayer, 63, has served as Executive Vice President for Risk at The Mount Sinai Medical Center (“Mount Sinai”), one of the country’s oldest and largest voluntary teaching hospitals, since September 2008. He is a Dr. Charles M. and Marilyn Newman Professor and has served as Chairman and Director of the Department of Radiology at Mount Sinai since July 1995. Dr. Drayer served as the President and Executive Vice President for Hospital and Clinic Affairs at Mount Sinai from November 2003 until September 2008. He is a Fellow of both the American Academy of Neurology and the American College of Radiology, serving on the Board of Chancellors of the latter. Dr. Drayer also serves on the Board of Directors of the Radiological Society of America. He is presently President-elect of the RSNA. Dr. Drayer is a former president of the American Society of Neuroradiology (ASNR), a founder of the Neuroradiology Education and Research Foundation of ASNR, as well as a former president of the New York Roentgen Society. Dr. Drayer holds an A.B. in Political Science from the University of Pennsylvania and received his M.D. from the Chicago Medical School at the University of Health Sciences in Chicago. Dr. Drayer has also served on the faculty and in leadership positions of three research-oriented medical schools, and has authored more than 200 journal articles and similar publications, 41 book chapters and two books and is an internationally recognized expert in the areas of radiology and neuroradiology.

Forward-Looking Statements

Any statements about future expectations, plans, and prospects for the Company, including statements containing the words “believes,” “anticipates,” “plans,” “expects,” and similar expressions, constitute forward-looking

statements within the meaning of the Private Securities Litigation Reform Act of 1995. Actual results may differ materially from those indicated by such forward-looking statements as a result of various important factors, including risks relating to product development and commercialization, limited demand for the Company’s products, risks associated with competition, uncertainties associated with regulatory agency approvals, competitive pricing pressures, downturns in the economy, the risk of potential intellectual property litigation, and other factors discussed in our most recent quarterly report filed with the Securities and Exchange Commission. In addition, the forward-looking statements included in this presentation represent the Company’s views as of the date of this document. While the Company anticipates that subsequent events and developments will cause the Company’s views to change, the Company specifically disclaims any obligation to update these forward-looking statements. These forward-looking statements should not be relied upon as representing the Company’s views as of any later date.

About Ramius LLC

Ramius LLC is an investment advisor that manages assets in a variety of alternative investment strategies. Ramius LLC is headquartered in New York with offices located in London, Luxembourg, Tokyo, Hong Kong and Munich.

About Analogic

Analogic Corporation is a growth oriented high-technology signal and image-processing company, providing products and services to original equipment manufacturers (OEMs) and end users in growing medical diagnostics and security markets worldwide. The Company is recognized worldwide for advancing the state of the art in automatic explosives detection, computed tomography (CT), digital radiography (DR), ultrasound, magnetic resonance imaging (MRI), and advanced signal processing. For more information, visit www.analogic.com.

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