<PAGE>   1
                                                            EXHIBIT (10)(b)(vii)


                              EMPLOYMENT AGREEMENT

This Agreement is made as of September 26, 1996 by and between American Science
and Engineering, Inc. (the "Company"), a Massachusetts corporation having its
principal place of business in Billerica, Massachusetts, and Ralph S. Sheridan
(the "Executive").

The Company desires to retain the services of the Executive, and the Executive
is willing to render such services in accordance with the terms hereinafter set
forth.

The Board of Directors of the Company (the "Board") has by appropriate
resolutions authorized the employment of the Executive as provided for in this
Agreement.

Accordingly, the Company and the Executive agree:

                                    ARTICLE I

1.1      Term. The term of this Agreement shall begin as of September 25, 1996
(the "Effective Date") and shall extend until September 25, 1999, unless earlier
terminated pursuant to Article V (the "Term"). The Executive's employment under
this Agreement may be extended or renewed solely by means of a written agreement
signed by the Executive and a representative of the Company expressly authorized
by the Board.

                                   ARTICLE II

2.1      President and Chief Executive Officer. The Executive shall be the
President and the Chief Executive Officer of the Company, shall report solely
and directly to the Board on all matters relating to the Executive's performance
of his duties, and shall perform such duties and responsibilities on behalf of
the Company and its subsidiaries as may be designated from time to time by the
Board.

The Executive shall devote his full business time and his best efforts, business
judgment, skill and knowledge exclusively to the advancement of the business and
interests of the Company and its subsidiaries and to the discharge of his duties
and responsibilities hereunder. The Executive will use his best judgment not to
accept any outside responsibilities that will jeopardize his ability to fulfill
his responsibilities as President and Chief Executive Officer of the Company.

One or more members of the Compensation Committee of the Board shall meet with
the Executive at least annually during the Term, shall review with him the
Company's performance to date, shall discuss his management accomplishments as
well as any areas requiring improvement, and shall review his base compensation
as provided in Section 3.1.

2.2      Director. Subject to the vote of the stockholders at subsequent annual
meetings, the Executive shall continue to serve as a Director of the Company
during the term of this Agreement.



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<PAGE>   2
                                   ARTICLE III

3.1      Base Salary. For services rendered by the Executive under this
Agreement during the Term, the Company shall pay or cause to be paid to the
Executive, in accordance with the Company's normal payroll practices for senior
executives of the Company, base salary ("Base Salary") for the initial year of
employment at the annual rate of $240,000. The Base Salary will be formally
reviewed on an annual basis by the Compensation Committee and increased in the
ensuing years if the Committee determines that an increase is warranted.

3.2      Bonuses. In addition to Base Salary, the Executive shall be paid an
annual bonus not to exceed $230,000 annually, which bonus will be established by
the Compensation Committee (the "Bonus"). Promptly following the execution of
this Employment Agreement, the Company and the Executive will meet to establish
the performance goals upon which the award of the Bonus for the first year of
employment pursuant to this Employment Agreement (the "First Bonus Period") will
be determined. Seventy-five percent of the Bonus will be based upon an
agreed-upon pre-tax income goal plus the amount expended by the Company in such
year for research and development ("Target Income"). Target Income will be
adjusted each year by the mutual consent of the Compensation Committee and the
Executive. Twenty-five percent of the Bonus will be based on personal
performance goals which will be established annually by the Compensation
Committee and the Executive promptly after the execution of this Employment
Agreement and revised on an annual basis in each subsequent year of this
Employment Agreement. During each subsequent year of employment pursuant to the
terms of this Employment Agreement ("Subsequent Bonus Periods"), the Chairman of
the Board and the Executive shall meet periodically to discuss the Executive's
progress concerning these goals. Promptly after the end of each such Subsequent
Bonus Period, the Compensation Committee shall meet to discuss the Executive's
performance with regard to such goals and shall, in its discretion, determine
the amount, if any, of the Bonus to be paid to the Executive for such Subsequent
Bonus Period. For the purpose of this determination, the goals shall be laddered
so that attainment of some, but not all, goals will give rise to the payment of
a partial Bonus.

3.3      Stock Options.

         Grant of Unconditional Option. The Company grants to the Executive a
non-statutory stock option (the "Unconditional Option"), in the form of the
stock option agreement attached hereto as Exhibit B, to purchase in the
aggregate 225,000 shares of the Company's Common Stock. The purchase price per
share of the 225,000 shares covered by the Unconditional Option shall be the
fair market value of the stock as of the date of the execution of the stock
option agreement granting the Unconditional Option. The option to acquire the
first seventy five thousand shares will vest on the first anniversary date of
the commencement of this Employment Agreement. The option to acquire an
additional 75,000 shares will vest on the second anniversary and a final option
to acquire 75,000 shares will vest on the third anniversary of this Employment
Agreement. The stock options shall be subject to termination only if employment
is terminated by the Company for Cause or if the Executive voluntarily requests
termination prior to September 25, 1999 for reasons other than for Good Reason.
All stock options will immediately vest if the Executive terminates employment
for Good Reason as defined in Article V 5.1(b)


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<PAGE>   3
herein or if the Company or all or substantially all of its assets or stock are
acquired by a third party or by merger, consolidation or otherwise. 

3.4      Securities Act of 1933. The Company agrees to register the shares
subject to the stock options referred to in this Article III pursuant to the
Securities Act of 1933, as promptly as practicable.

                                   ARTICLE IV

4.1      Benefits During the Term. During the Term, the Executive will be
covered by and receive benefits not specifically dealt with in this Agreement
(such as the payment provisions set forth in Article V in the event of
termination of employment, which are intended to be exclusive) under the benefit
plans and programs maintained by the Company from time to time for its senior
executives. The Executives shall also be entitled to such other perquisites of
office as are generally provided from time to time by the Company to its senior
executive officers. The Executive shall be reimbursed for all reasonable
out-of-pocket expenses reasonably incurred by him in the performance of his
duties hereunder, upon submission of appropriate documentation in accordance
with the Company's written policies.

4.2      Automobile. The Company shall provide the Executive, at his request,
with an automobile for his use during the Term. The Company will pay for all
expenses associated with the Executive's business use of the automobile. At the
end of the Term, the Executive shall return the automobile to the Company in
substantially the same condition as on the date he first received it, reasonable
wear and tear excepted.

                                   ARTICLE V

5.1      Termination by the Company without Cause or by the Executive for Good
         Reason.

(a)      The Company may, upon written notice to the Executive, immediately
terminate the Executive's employment hereunder without Cause. For purposes of
this Article V, "Cause" shall mean:

         (i)      the Executive's willful and continuing failure to perform his
                  duties in the course of his employment under this Agreement,
                  which failure is not cured by the Executive within 30 days
                  after notice specifically describing such failure is provided
                  in writing by the Company to the Executive; or

         (ii)     the conviction of the Executive for, or his plea of nolo
                  contendere to, a felony or any other crime which involves
                  fraud, dishonesty or moral turpitude.

(b)      The Executive may, upon 15 days' written notice to the Company,
terminate his employment hereunder for Good Reason. For purposes of this Article
V, "Good Reason" shall mean:


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<PAGE>   4
         (i)      the assignment of the Executive of any duties, inconsistent in
                  any respect with the Executive's position as the President and
                  Chief Executive Officer of the Company or any other action by
                  the Company which results in a diminution in such position,
                  authority, duties or responsibilities, excluding for this
                  purpose an isolated, insubstantial and inadvertent action not
                  taken in bad faith and which is remedied by the Company within
                  30 days after receipt of written notice thereof given by the
                  Executive, provided, however, that any change or diminution of
                  the business of the Company or of any subsidiary or
                  subsidiaries of the Company, including without limitation the
                  sale or transfer of such subsidiaries, or any or all of their
                  assets, shall not constitute "Good Reason";

         (ii)     any failure of the Company to comply with any of the
                  provisions of the Employment Agreement, other than an
                  insubstantial failure not occurring in bad faith and which is
                  remedied by the Company within 30 days after receipt of
                  written notice thereof given by the Executive;

         (iii)    failure of the Company and the Executive, bargaining in good
                  faith, to agree upon performance goals pursuant to Section
                  3.2(b) and an annual Base Salary for the second and third year
                  of this contract;

         (iv)     any failure of the Company to obtain a satisfactory agreement
                  from any successor to all or substantially all of the business
                  or assets of the Company to assume and agree to perform this
                  Agreement; or

         (v)      any purported termination by the Company of the Executive's
                  employment otherwise than as expressly permitted by the
                  Employment Agreement.

(c)      In case of any termination of the Executive's employment hereunder
without Cause or for Good Reason (as defined above), the Company shall pay to
the Executive (or in the event of his death, his designated beneficiary or his
estate, as the case may be): (1) a sum equal to the Executive's then annual Base
Salary in cash payable at the times such sum would have been paid to the
Executive if he had remained in the employ of the Company and was entitled to
receive such sum in the form of Base Salary during the 12-month period following
his termination of employment, and (2) the amount the Executive earned in Bonus
payments and, if such termination occurs prior to September 25, 1997, the value
of any stock received in the year previous to such termination, payable at such
time such Bonus would have been paid had the Executive remained in the employ of
the Company. In addition, any unvested stock options outstanding on the date of
the Executive's termination of employment shall become vested and exercisable in
accordance with their terms. The failure of the Company to extend the term of
this Employment Agreement or any extension of this Employment Agreement for an
additional term of not less than one year on terms no less favorable to the
Company than those contained herein and if requested by the Executive shall be
deemed a termination for Good Reason requiring the Company to make the severance
and benefits to the Executive as described in this Section 5.1(c).

5.2      Termination by the Company for Cause or by the Executive Other Than for
Good Reason. During the Term, the Company, by action of the board, may terminate
the Executive's


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<PAGE>   5
employment hereunder for Cause by written notice to the Executive stating in
detail the reasons for such termination. During the Term, the Executive may, by
written notice to the Board, terminate his employment hereunder other than for
Good Reason. In the event of any such termination for Cause or other than for
Good Reason (and other than by reason of his death or disability), the Executive
shall not be entitled to any unpaid bonus that may have been earned through such
date, nor shall he be entitled to exercise the Unconditional Option which have
not been vested.

5.3      Termination for Disability.

(a)      The Company may terminate the Executive's employment hereunder, upon
notice to him, in the event that he becomes disabled through any illness,
injury, accident or condition of either a physical or psychological nature and,
as a result, is unable to perform substantially all of his duties and
responsibilities hereunder for any consecutive 60 day period.

(b)      If any question shall arise as to whether during any period the
Executive is disabled through any illness, injury, accident or condition of
either a physical or psychological nature so as to be unable to perform
substantially all of his duties hereunder, the Executive may, and at the request
of the Company shall, submit to a medical examination by a physician mutually
acceptable to the Company and the Executive or his guardian to determine whether
the Executive is so disabled, and such determination shall for the purposes of
this Agreement be conclusive of the issue. In the event that a physician cannot
be selected by mutual agreement, a physician shall be appointed by the
Massachusetts Medical Society.

(c)      If the Executive's employment hereunder is terminated as the result of
his disability, the Executive will receive his Base Salary through the date of
termination, together with any unpaid Bonus that may have been earned through
such date, but shall otherwise look solely to the Company's disability insurance
policy or policies for compensation (except that any waiting period for
eligibility purposes shall be waived by the Company).

5.4      Termination in the Event of Death. In the event of the Executive's
death during the Term, his employment hereunder shall be deemed to have
terminated for all purposes of this Agreement on his date of death and neither
his designated beneficiary nor his estate shall be entitled to any of the
compensation or benefits provided for herein, other than the Executive's Base
Salary, and any unpaid Bonus earned by the Executive, through his date of death
(it being understood that his designated beneficiary or estate, as the case may
be, shall be entitled to receive the life insurance benefits available under the
Company's executive life insurance policies), and to exercise the Unconditional
Option to the extent exercisable on his date of death, within one year of his
date of death, but not later than the expiration date of such Option.

                                   ARTICLE VI

6.1      Designation of a Beneficiary or Beneficiaries. The Executive may
designate in a writing filed with the Company one or more persons (including his
estate) as the beneficiary or beneficiaries of the benefits provided for under
the Agreement after the Executive's death. The Executive may change his
designation of beneficiary or beneficiaries from time to time, and the


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<PAGE>   6
last designation in writing filed with the Company prior to his death will
control. If the Executive has failed to file a designation of beneficiary at the
time of the Executive's death, or if all designated beneficiaries have
predeceased him, the amounts payable under this Agreement shall be paid to the
Executive's estate.

                                   ARTICLE VII

7.1      Notices. All notices required by this Agreement shall be in writing and
delivered by hand, by overnight courier against receipt, by registered or
certified mail, postage prepaid, or by telephonic facsimile transmission duly
acknowledged, and, in the case of the Executive, addressed to the Executive at
79 Byron Road, Weston, MA 02193, or, in the case of the Company, to its
principal office, addressed to the attention of the Clerk. Either party may from
time to time designate a new address by notice given in accordance with this
Paragraph 7.1.

7.2      Assignment. The Company may not assign all or any part of its
obligation under this Agreement. The Company will require any successor (whether
direct or indirect, by purchase, merger, consolidation or otherwise) to all or
substantially all of the business or assets of the Company expressly to assume
and agree to perform this Agreement to the same extent that the Company would be
required to perform it if no succession had taken place. As used in this
Agreement, unless the context requires otherwise, the "Company" shall mean the
Company as defined above or any successor to its business or assets as aforesaid
which assumes and agrees to perform this Agreement, by operation of law, or
otherwise. This Agreement shall inure to the benefit of and be enforceable by
and binding upon (i) any such successor and (ii) the Executive's personal or
legal representatives, executors, administrators and designated beneficiaries.

7.3      Entire Agreement. This Agreement contains the entire agreement between
the parties and supersedes all prior oral and written agreements, understandings
and commitments between the parties relating to this Agreement. No amendment to
this Agreement shall be made except by a written instrument signed by both
parties.

7.4      Proprietary Information and Non Competition. The Executive
acknowledges and stipulates that, in the performance of his duties hereunder,
the Executive is entrusted by the Company and its subsidiaries with confidential
and secret information of a proprietary nature, including, but not limited to
scientific data, financial and statistical information regarding affairs of the
Company and its subsidiaries, supplier and subcontractor lists, price and cost
information, business plans and programs, expansion plans, data, methods,
techniques, marketing data, designs and know-how, developed or obtained by the
Company or its subsidiaries (collectively, "Proprietary Information"). The
Executive may not at any time use, or cause or permit others to use, the
Proprietary Information except in the performance of his duties for the Company
and shall not directly or indirectly disclose at any time either during the Term
or for a period of two years thereafter any such Proprietary Information to any
third party other than in the course of the performance of his duties for the
Company. "Proprietary Information" shall not include any (i) information which
is part of the public domain (other than by act of the Executive), or (ii) any
information required to be disclosed by law.


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<PAGE>   7
         Executive agrees that, subsequent to the termination of this Employment
Agreement, unless terminated by the Company without Cause or by the Executive
for Good Reason, Executive shall not:

                  (i)      request, cause or encourage any person or entity to
                           cancel, terminate or refuse to enter into any
                           business relationship with the Company;

                  (ii)     during the one-year period following such termination
                           solicit or encourage, directly or indirectly, any
                           employee of the Company to leave the employment of
                           the Company; or

                  (iii)    during the one-year period following such termination
                           either engage in any business or undertake employment
                           or consulting services in the area of x-ray detection
                           devices which would directly compete with devices
                           then manufactured and/or marketed by the Company.

The provisions of this Section 7.4 shall continue in effect after the Term.

7.5      Partial Invalidity. If for any reason any provision of this Agreement
shall be held invalid in whole or in part, such invalidity shall not affect such
provision to the extent not so held invalid, nor any other provisions of this
Agreement not held so invalid, and such provisions and all other such provisions
shall to the full extent be consistent with law continue in full force and
effect.

7.6      Withholding. All payments made by the Company under this Agreement
shall be reduced by any tax or other amounts required to be withheld by the
Company under applicable law.

7.7      Governing Law. This Agreement shall be construed and enforced under and
be governed in all respects by the law of the Commonwealth of Massachusetts,
without regard to the conflict of law principles thereof.

IN WITNESS WHEREOF, the Company has caused this instrument to be executed on its
behalf by a duly authorized officer and the Executive has executed this
instrument, all as of the date set forth above.

                                       AMERICAN SCIENCE AND ENGINEERING, INC.


                                       By: /s/ Jeffrey Bernfeld
                                           ----------------------------------
                                           Jeffrey Bernfeld, Vice President

                                           /s/ Ralph S. Sheridan 
                                           ----------------------------------
                                           Ralph S. Sheridan


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<PAGE>   8
                                   EXHIBIT B


                     AMERICAN SCIENCE AND ENGINEERING, INC.

                      NON-STATUTORY STOCK OPTION AGREEMENT
                            Covering 225,000 Shares
                                of Common Stock

AGREEMENT made as of this 24th day of October, 1996, by and between AMERICAN
SCIENCE AND ENGINEERING, INC., a corporation duly organized under the laws of
The Commonwealth of Massachusetts (the "Company"), and Ralph S. Sheridan, the
President and Chief Executive Officer of the Company (the "Optionee").

                                WITNESSETH THAT:

WHEREAS, the Company and the Optionee have entered into an Employment Agreement
dated as of September 25, 1996 (the "Employment Agreement"), providing among
other things for the employment of the Optionee as President and Chief Executive
Officer of the Company and the grant of non-statutory stock options to the
Optionee; and

WHEREAS, the Board of Directors of the Company has appointed the Compensation
Committee to administer this Agreement (the Board of Directors, such committee
or any successor to such committee being hereinafter referred to as the
"Board");

NOW, THEREFORE, for and in consideration of the mutual covenants hereinafter set
forth and for other good and valuable consideration, it is agreed as follows:

1.       GRANT OF OPTION. The Company hereby grants to the Optionee a
non-statutory stock option (the "Option") to purchase 225,000 shares of its
common stock at $14.00 per share, being 100% of the fair market value of such
stock on the date hereof. The Optionee's right to purchase said stock shall be
exercised in the manner and subject to the terms and conditions hereinafter
provided. The Company shall, at all times while the Option is in force, reserve
such number of shares of common stock as will be sufficient to satisfy the
requirements of this Agreement.

2.       TIME OF EXERCISE OF THE OPTION.

(a) Subject always to the provisions of Sections 2(b) and 3 and the terms and
conditions of the Employment Agreement: (i) the Option may not be exercised
prior to September 25, 1997; and (ii) on and after September 25, 1997, the
Option may be exercised as to seventy-five thousand shares covered thereby. On
and after September 25, 1998, the Option may be exercised as to an additional
seventy-five thousand shares covered thereby. On and after September 25, 1999,
the Option may be exercised as to the remaining seventy-five thousand shares
covered thereby.


                                      B-1
<PAGE>   9
(b) Notwithstanding Section 2(a), the Option may be exercised as to all of the
shares covered thereby upon the occurrence of a Change in Control of the
Company. For the purposes of this subsection 2(b), a "Change in Control" of the
Company shall be deemed to have occurred if:

         (i)      any person (as defined in Section 13(d) or 14(d)(2) of the
                  1934 Act) shall have become the beneficial owner of 50 percent
                  or more of the combined voting power of the Company's voting
                  securities;

         (ii)     the Continuing Directors and the Optionee shall have ceased
                  for any reason to constitute a majority of the Board of
                  Directors of the Company. For this purpose, a "Continuing
                  Director" shall include member of the Board of Directors of
                  the Company as of September 26, 1996 and any person nominated
                  for election to the Board of Directors of the Company by a
                  vote of a majority of the then Continuing Directors;

         (iii)    the stockholders approve the complete liquidation or
                  dissolution of the Company, or

         (iv)     the stockholders approve by the requisite vote any of the
                  following transactions: (x) a merger or consolidation of the
                  Company (except for a merger in respect of which no vote of
                  the stockholders of the Company is required); (y) a sale,
                  lease, exchange, mortgage, pledge, transfer or other
                  disposition (in one transaction or a series of transactions),
                  whether as part of a dissolution or otherwise, of assets of
                  the Company or of any direct or indirect majority-owned
                  subsidiary or the Company (other than to any direct or
                  indirect wholly-owned subsidiary or to the Company) having an
                  aggregate market value equal to 50% or more of either that
                  aggregate market value of all of the assets of the Company
                  determined on a consolidated basis or the aggregate market
                  value of all the outstanding stock of the Company; or (z) a
                  proposed tender or exchange offer for 50% or more of the
                  outstanding voting stock of the Company.

(c)      Notwithstanding Section 2(a) and subject to Section 4 hereof, the
Option may be exercised as to all of the shares covered thereby in the event
that the Optionee's employment shall have been terminated without Cause or for
Good Reason as provided by Section 5.1 of the Employment Agreement.

(d)      Notwithstanding any of the foregoing, the Option shall not be
exercisable after the expiration of 10 years from the date hereof.

3.       METHOD OF EXERCISE.

(a) Stock purchased under the Option shall at the time of exercise be paid in
full. The Option may be exercised from time to time by written notice to the
Company stating the number of shares with respect to which the Option is being
exercised, and the time of the delivery thereof, which time shall be at least
five business days after the giving of such notice unless an earlier


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<PAGE>   10
date shall have been mutually agreed upon. At the time specified in such notice,
the Company shall, without transfer or issue tax to the Optionee (or other
person entitled to exercise the Option), deliver to the Optionee (or other
person entitled to exercise the Option) at the main office of the Company, or
such other place as shall be mutually acceptable, a certificate or certificates
for such shares (as the number of such shares may be reduced subject to
subsection (c) below) out of theretofore authorized but unissued shares or
reacquired shares of its common stock, as the Company may elect, against payment
of the Option price in full for the number of shares to be delivered by
certified or bank cashier's check or the equivalent thereof acceptable to the
Company (including, but not limited to, shares of capital stock of the Company);
provided, however, that the time of such delivery may be postponed by the
Company for such period as may be required for it with reasonable diligence to
comply with any applicable listing requirements of any national securities
exchange. If the Optionee (or other person entitled to exercise the Option)
fails to accept delivery of and pay for all or any part of the number of shares
specified in such notice upon tender of delivery thereof, his right to exercise
the Option with respect to such undelivered shares may be terminated by the
Board.

(b) Promptly upon receipt of the written notice provided for in subsection (a)
above, the Board shall, with the assistance of appropriate employees of the
Company, determine if any portion of such intended exercise (the "Disallowance
Portion") may reasonably be expected to result in receipt of compensation by the
Optionee as to which the Company will not be allowed to claim a deduction in
respect of the Company's taxable year during which such exercise occurs, when
the amount of remuneration attributable to such exercise is taken together with
the Optionee's base salary and the reasonably likely cash and stock bonuses
payable to him in respect of such taxable year, pursuant to Section 162(m) of
the Internal Revenue Code of 1986, as amended, and the regulations thereunder.

(c) The Board shall promptly notify the Optionee of its determination as to the
Disallowance Portion, and, subject to subsection (d) below, the exercise
contemplated by the written notice in subsection (a) shall be deemed to be
reduced by the number of shares in the Disallowance Portion.

(d) Notwithstanding the foregoing, in the event of a Change in Control (as
defined in Section 2(b), the Disallowance Portion shall be deemed to be zero (0)
shares.

4.       TERMINATION OF EMPLOYMENT. The Optionee may, at any time within three
months after the date of termination of his employment with the Company or any
of its subsidiaries for any reason except death, but not later than the date of
expiration of the Option, exercise the Option to the extent he was entitled to
do so on the date of termination; provided that the Optionee shall not be deemed
to be so entitled on the date of termination of his employment if he shall have
been terminated for Cause or other than for Good Reason as provided by Section
5.2 of the Employment Agreement. If the Option or any portion of the Option is
not so exercised, or if the Optionee shall be deemed not to be entitled to
exercise it or any portion thereof, the Option or portion thereof shall
terminate. However, the Option shall not be affected by any change in the duties
or position of the Optionee (including transfer to or from


                                      B-3
<PAGE>   11
a subsidiary) so long as the Optionee continues in the employ of the Company or
one of its subsidiaries.

Nothing in this Agreement shall confer on the Optionee any right to continue in
the employ of the Company or its subsidiaries; affect the right of the Company
or its subsidiaries to terminate the Optionee's employment at any time; or be
deemed a waiver or modification of any provision contained in the Employment
Agreement of any other agreement between the Optionee and the Company or any
such subsidiary.

5.       EXERCISE BY REPRESENTATIVE, ETC. If the Optionee dies while in the
employ of the Company or its subsidiaries or within three months after
termination of employment (except termination for Cause or other than for Good
Reason, as provided by Section 5.2 of the Employment Agreement), the person or
persons to whom the Option is transferred by will or the laws of descent and
distribution may, at any time within one year after the date of death but not
later than the date of expiration of the Option, exercise the Option to the
extent the Optionee was entitled to do so on the date of his death. If the
Option or any portion of the Option of the deceased Optionee is not so
exercised, it shall terminate.

6.       NON-TRANSFERABILITY OF OPTION. The Option may not be transferred except
by will or by the laws of the descent and distribution nor may it be otherwise
assigned, transferred, pledged, hypothecated or disposed of in any way (by
operation of law or otherwise) and it shall not be subject to execution,
attachment or similar process. During the lifetime of the Optionee, the Option
may be exercised only by the Optionee or the Optionee's duly appointed guardian
or personal representative.

7.       CHANGES IN COMMON STOCK. In the event of any reorganization,
recapitalization, stock split, stock dividend, merger, consolidation,
combination of shares or other change affecting the Company's common stock, the
Board shall make adjustments in the number and kind of securities to be subject
to the Option, such adjustments to be consistent with adjustments made with
respect to options held by other employees and directors of the Company. Any
such adjustment made by the Board shall be conclusive. This Agreement shall not
affect the right of the Company or any of its subsidiaries to reclassify,
recapitalize or otherwise change its capital or debt structure or to merge,
consolidate, convey any or all of its assets, dissolve, or liquidate, wind up or
otherwise reorganize.

8.       RESTRICTION ON ISSUANCE OF SHARES. The Company shall not be obligated
to sell or issue any shares pursuant to the Option unless the shares with
respect to which the Option is being exercised are at that time effectively
registered or exempt from registration under the Securities Act of 1933, as
amended.

9.       RIGHTS AS A STOCKHOLDER. The Optionee shall have no rights as a
stockholder with respect to any shares covered by the Option until the date of
issuance of a stock certificate to the Optionee for such shares. No adjustment
shall be made for dividends or other rights for which the record date is prior
to the date such stock certificate is issued.


                                       B-4
<PAGE>   12
10.      WITHHOLDING. The Company or any subsidiary that employs the Optionee
shall have the right to deduct any sums that federal, state or local tax law
requires to be withheld with respect to the exercise of the Option. In the
alternative, the Optionee or other person exercising the Option may elect to pay
such sums to the employer corporation either by check or with capital stock of
the Company by delivering written notice of that election to the Clerk of the
Company no less than 30 days nor more than 60 days prior to exercise. There is
no obligation hereunder that the Optionee be advised of the amount which the
employer corporation or the Company will be required to withhold.

11.      INTERPRETATION OF PLAN AND OPTION. As used herein the term "subsidiary
of the Company" shall mean a subsidiary corporation as defined in Section 425 of
the Internal Revenue Code of 1986. In all other respects, questions of
interpretation and application of this Agreement shall be determined by a
majority of the Board, and the determinations of such majority shall be final
and binding upon all persons.

EXECUTED as a sealed instrument at Cambridge, Massachusetts, as of the date
appearing in the first paragraph of this Agreement.

                                          AMERICAN SCIENCE AND
                                          ENGINEERING, INC.


                                          By: /s/ Jeffrey Bernfeld
                                              --------------------------------
                                              Jeffrey Bernfeld
                                              Vice President & General Counsel

                                              /s/ Ralph S. Sheridan
                                              --------------------------------
                                              Ralph S. Sheridan



                                       B-5