Exhibit 99.1

January 23, 2012

Gina Consylman

14 Mt. Vernon Street

Charlestown, MA 02129

Dear Gina:

I am delighted to offer you the position of Vice President and Corporate Controller for Analogic Corporation. I am excited about the prospect of your joining Analogic and look forward to your leadership in helping build a strong future for our Company.

The following provides the terms and conditions of your employment offer set forth in this letter Agreement (the “Agreement”):

Start Date. Your employment will commence on February 27, 2012.

Reporting Relationship. You will report directly to me, Michael Levitz, Senior Vice President and CFO.

Base Salary. Your annualized base salary (the “Base Salary”) will be $230,000 per year. Your review will occur in September as part of the normal year-end Company process for fiscal year 2012. Salary will be paid bi-weekly in accordance with the Company’s normal payroll practices.

Annual Performance Bonus. Beginning with the Fiscal Year 2012, you will be eligible for a target award (the “Target Bonus”) equal to 35% (and a “Maximum Bonus” of 70%) of your base salary paid during the plan year. Awards will be paid in accordance with the provisions of the Analogic Annual Incentive Plan (AIP). More information about the AIP and the specific financial metrics in the Plan will be provided to you after your Start Date.

One Time Equity Grant. As soon as practical after your start date, subject to Compensation Committee approval, you will receive a one-time grant of 3,000 Analogic Restricted Stock Units (RSUs), with the award vesting 33% per year beginning on the first anniversary of the grant date.

Long Term Incentives. You will be eligible to participate in the Company’s Long Term Incentive Program (the “LTIP”). The grant value of your award under the FY2012 LTIP will be 80% of annual salary, pro-rated for the number of months you

work during the fiscal year. The FY2012 LTIP is comprised of three components of equal value – Stock options, Total Shareholder Return Restricted Stock Units (TSR RSUs), and Non-GAAP Earnings Per Share Restricted Stock Units (Non-GAAP EPS RSUs). Your award will be subject to the approval of the Compensation Committee. Our Standard RSU agreements include a non-competition provision.

Benefits. You will be eligible to participate in the Company’s standard benefit program generally applicable to similarly situated executives which includes medical, dental and life insurance, short and long-term disability protection and participation the Company’s 401(k) plan. The full range of benefits for you and the family is summarized in the enclosed Employee Benefits Summary for 2012. Note that the Company reserves the right to change or amend its benefit plans it offers to employees at any time.

Vacation. You will be entitled to accrue up to four (4) weeks of paid vacation each year of employment plus sick leave on the same basis as all other executives of the Company.

Non-Qualified Deferred Compensation (NQDC). The Analogic NQDC provides for additional deferred compensation opportunities for executive employees. Specifically, the plan provides for: (1) the opportunity to defer up to 25% of base salary and 100% of annual cash bonuses into a variety of fund options and (2) a 4% match on all contributions that exceed the 401(k) limits should your compensation exceed the IRC 401(a) Annual Compensation Limit.

Prior Agreements. You represent and warrant that you are not bound by any agreement with a previous employer or other party that you would breach by accepting employment with the Company or performing your duties as an employee of the Company. You further represent and warrant that, in the performance of your duties with the Company, you will not utilize or disclose any confidential information in breach of an agreement with a previous employer or any other party.

Entire Agreement. This Agreement constitutes the entire agreement between you and the Company with respect to the subject matter hereof, and it supersedes all previous communications, representations, or agreements, either oral or written. There are no representations or warranties other than those contained in this Agreement, and in entering into this Agreement, you acknowledge that you have not relied on any representations, statements, or warranties not expressly set forth in this Agreement. No addition to or modification of this Agreement shall be binding unless made in writing and signed by you and a duly authorized Company representative.

Nature of Employment. Notwithstanding anything in this Agreement to the contrary, your employment with the Company is on an “at-will” basis, meaning that either you or the Company may terminate the employment relationship at any time, for any reason, with or without cause and with or without notice, subject to the severance provisions described above.

Contingencies. This offer of employment at will is extended to you contingent upon your acceptance of the following:

a) That you understand and accept the requirements of our corporate policy governing Conflict of Interest. A copy of this policy is enclosed.

b) That you understand our agreement concerning Proprietary Information and Inventions and indicate your acceptance by signature thereon.

It will be necessary to pass a drug test for certain illicit substances, pass a background check, which includes credit and court records, and I-9 proof of U.S. employment eligibility. Documents that explain these requirements are enclosed.

Gina, I certainly hope that you will accept this challenging opportunity and I enthusiastically look forward to working with you in your new role at Analogic.

Accepted and agreed to on this 24 day of January, 2012.