<PAGE>   1
                                    FORM 10Q
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549



              [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                For the quarterly period ended September 27, 1996

                                       OR

              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                 For the transition period from             to

                          Commission File Number 1-6549

                     American Science and Engineering, Inc.
             (Exact name of Registrant as specified in its charter)

          Massachusetts                                 04-2240991      
(State or other jurisdiction of                      (I.R.S. Employer
incorporation or organization)                       Identification No.)

        829 Middlesex Turnpike
       Billerica, Massachusetts                             01821
(Address of principal executive offices)                  (Zip Code)

                                 (508) 262-8700
              (Registrant's telephone number, including area code)


      (Former name, former address and former fiscal year, if changed since
                                  last report)

Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months, and (2) has been subject to such filing requirements
for the past 90 days.

                          Yes   X            No
                               ---              ---

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date

<TABLE>
<CAPTION>

                                                      Outstanding at
    Class of Common Stock                             Sept. 27, 1996
    ---------------------                             --------------
    <S>                                               <C>
    $.66 2/3 par value                                  4,550,276
</TABLE>


                               Page 1 of 11 Pages
                     The Exhibit Index is Located at Page 11
<PAGE>   2
                     AMERICAN SCIENCE AND ENGINEERING, INC.
                         PART I - FINANCIAL INFORMATION
                 CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (Unaudited)

Dollars and shares in Thousands, except per share amounts

<TABLE>
<CAPTION>
                                                     For The Three Months Ended   For The Six Months Ended
                                                     --------------------------   ------------------------
                                                       Sept. 27,     Sept.29,        Sept. 27,      Sept. 29,
                                                         1996          1995            1996           1995
                                                         ----          ----            ----           ----
<S>                                                  <C>             <C>            <C>          <C>    
NET SALES AND CONTRACT REVENUE                       $  6,685        $  3,882        $ 13,384        $  7,399
                                                     --------        --------        --------        --------
COSTS AND EXPENSES:
  Cost of sales and contracts                           4,329           2,577           8,937           5,030
  Selling, general and administrative expenses          1,473             962           2,872           1,921
  Research and development                                350             128             594             183
                                                     --------        --------        --------        --------
  Total costs and expenses                              6,152           3,667          12,403           7,134
                                                     --------        --------        --------        --------
OPERATING INCOME                                          533             215             981             265
                                                     --------        --------        --------        --------
OTHER INCOME (EXPENSE):
   Interest, net                                           24             (12)             71              (9)
   Other, net                                             (87)            (48)           (156)            (49)
                                                     --------        --------        --------        --------
   Total other income (expense)                           (63)            (60)            (85)            (58)
                                                     --------        --------        --------        --------
INCOME BEFORE PROVISION
  FOR INCOME TAXES                                        470             155             896             207

PROVISION FOR INCOME TAXES                                 19            --                39            --
                                                     --------        --------        --------        --------
NET INCOME                                           $    451        $    155        $    857        $    207
                                                     ========        ========        ========        ========
INCOME PER COMMON SHARE AND
  COMMON EQUIVALENT SHARE                            $    .09        $    .04        $    .18        $    .05
                                                     ========        ========        ========        ========
INCOME PER COMMON SHARE,
  ASSUMING FULL DILUTION                             $    .09        $    .04        $    .18        $    .05
                                                     ========        ========        ========        ========
DIVIDENDS PAID PER SHARE                                 NONE            NONE            NONE            NONE

SHARES USED IN INCOME PER SHARE
  AND COMMON EQUIVALENT SHARES                          4,869           4,409           4,791           4,292
                                                     ========        ========        ========        ========
SHARES USED IN INCOME PER COMMON
  SHARE, ASSUMING FULL DILUTION                         4,891           4,409           4,801           4,292
                                                     ========        ========        ========        ========
</TABLE>

The accompanying notes are an integral part of these condensed consolidated
financial statements.

                                       -2-
<PAGE>   3



AMERICAN SCIENCE AND ENGINEERING, INC.
CONDENSED CONSOLIDATED BALANCE SHEETS

Dollars in thousands
<TABLE>
<CAPTION>
                                                               Sept. 27, 1996      Mar. 29, 1996
                                                               --------------      -------------
                                                                (Unaudited)
<S>                                                               <C>                 <C>     
ASSETS                CURRENT ASSETS:
                      Cash and cash equivalents                   $  2,244            $  3,377
                      Accounts receivable, net                       5,666               3,875
                      Unbilled costs and fees, net                   1,038               1,258
                      Inventories                                    4,063               4,314
                      Prepaid expenses and other current
                         assets                                        303                 278
                      Deferred income taxes                             10                  10
                                                                  --------            --------
                      Total current assets                          13,324              13,112
                                                                  --------            --------

                      NON CURRENT ASSETS:
                      Deposits                                         110                 257
                      Property and equipment, net
                         of accumulated depreciation of
                         $8,669 at Sept. 27,1996 and
                         $8,507 at March 29,1996                     1,184                 926
                                                                  --------            --------

                                                                  $ 14,618            $ 14,295
                                                                  ========            ========
</TABLE>


The accompanying notes are an integral part of these condensed consolidated
financial statements.

                                       -3-
<PAGE>   4
                     AMERICAN SCIENCE AND ENGINEERING, INC.
                CONDENSED CONSOLIDATED BALANCE SHEETS (CONTINUED)


Dollars in thousands
<TABLE>
<CAPTION>
                                                                    Sept. 27, 1996      Mar. 29, 1996
                                                                    --------------      -------------
                                                                      (Unaudited)
<S>                                                                   <C>                 <C>    
LIABILITIES &         CURRENT LIABILITIES:
STOCKHOLDERS'         Current maturities of obligations
INVESTMENT              under capital leases                          $    16             $    16
                      Accounts payable                                  2,849               2,021
                      Accrued legal                                       119                 128
                      Accrued salaries and benefits                       604                 496
                      Accrued warranty costs                              252                 178
                      Accrued commissions                                 335                 160
                      Deferred revenue                                    484                 375
                      Customer deposits                                   479               2,670
                      Other current liabilities                           361                 258
                                                                      -------             -------
                      TOTAL CURRENT LIABILITIES                         5,499               6,302
                                                                      -------             -------
                      NONCURRENT LIABILITIES:
                      Obligations under capital leases, net
                        of current maturities                              51                  59
                      Deferred compensation                               185                 192
                      Deferred rent                                       240                 231
                      Deferred income taxes                                10                  10
                                                                      -------             -------
                      TOTAL NONCURRENT LIABILITIES                        486                 492
                                                                      -------             -------

                      STOCKHOLDERS' INVESTMENT: Preferred stock,
                      no par value Authorized - 100,000 shares
                      Issued - None Common stock, $.66-2/3 par
                      value Authorized - 8,000,000 shares Issued
                      4,550,276 shares at Sept. 27,1996
                      and 4,500,627 shares at Mar. 29, 1996             3,034               3,001
                      Capital in excess of par value                   14,801              14,556
                      Accumulated deficit                              (8,432)             (9,290)
                                                                      -------             -------
                                                                        9,403               8,267
                      Note receivable-Officer                            (640)               (640)
                      Less: treasury stock -
                      67,707 shares at Sept. 27, 1996
                        and Mar. 29, 1996 at cost                        (130)               (126)
                                                                      -------             -------

                      TOTAL STOCKHOLDERS' INVESTMENT                    8,633               7,501
                                                                      -------             -------
                                                                      $14,618             $14,295
                                                                      =======             =======
</TABLE>

The accompanying notes are an integral part of these condensed consolidated
financial statements.

                               -4-
<PAGE>   5
              AMERICAN SCIENCE AND ENGINEERING, INC.
         CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                           (Unaudited)

Dollars in thousands
<TABLE>
<CAPTION>
                                                                               For the Six Months Ended
                                                                               ------------------------
CASH FLOWS FROM OPERATING ACTIVITIES:                                       Sept. 27, 1996    Sept. 29, 1995
                                                                            --------------    --------------
<S>                                                                              <C>            <C>    
Net income                                                                       $   857        $   207
Adjustments to reconcile net income to net cash provided by
(used for) operating activities:
   Depreciation and amortization                                                     162             98
   Provisions for contract, restructuring, inventory and warranty reserves           (56)           (46)
Changes in assets and liabilities
   Accounts receivable                                                            (1,861)        (1,645)
   Unbilled costs and fees                                                           220          1,117
   Inventories                                                                       301            169
   Prepaid expenses and other assets                                                 122           (150)
   Accounts payable                                                                  828           (510)
   Customer deposits                                                              (2,191)             2
   Accrued expenses and other current liabilities                                    636           (398)
   Noncurrent liabilities                                                              3              4
                                                                                 -------        -------
   Total adjustments                                                              (1,836)        (1,359)
                                                                                 -------        -------
Net cash provided by (used for) operating activities                                (979)        (1,152)
                                                                                 -------        -------
CASH FLOWS FROM INVESTING ACTIVITIES:
   Purchase of property and equipment                                               (420)            81
                                                                                 -------        -------
   Cash (used for) provided by investing activities                                 (420)            81
                                                                                 -------        -------
CASH FLOWS FROM FINANCING ACTIVITIES:
   Proceeds from borrowings                                                         --              813
   Repayment of officer note                                                        --             (650)
   Proceeds from exercise of stock options                                           274             11
   Proceeds from issuance of stock                                                  --              902
   Principal payments of capital lease obligations                                    (8)          (148)
                                                                                 -------        -------
   Cash (used for) provided by financing activities                                  266            928
                                                                                 -------        -------
NET DECREASE IN CASH AND CASH EQUIVALENTS                                         (1,133)          (143)
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                                   3,377            869
                                                                                 -------        -------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                                       $ 2,244        $   726
                                                                                 =======        =======
SUPPLEMENTAL DISCLOSURES OF CASH FLOW
INFORMATION:
   Interest paid                                                                 $     3        $    47
   Income taxes paid                                                             $    30        $  --
</TABLE>

The accompanying notes are an integral part of these condensed consolidated
financial statements.

                               -5-

<PAGE>   6
              AMERICAN SCIENCE AND ENGINEERING, INC.

    PREPARATION OF CONDENSED CONSOLIDATED FINANCIAL STATEMENTS

The condensed consolidated financial statements included herein have been
prepared by American Science and Engineering, Inc. (the Company) pursuant to the
rules and regulations of the Securities and Exchange Commission, and the annual
condensed consolidated financial statements are subject to year end audit by
independent public accountants. Certain information and footnote disclosures
normally included in financial statements prepared in accordance with generally
accepted accounting principles have been condensed or omitted pursuant to such
rules and regulations. The Company believes, however, that the disclosures are
adequate to make the information presented not misleading. It is suggested that
these condensed consolidated financial statements be read in conjunction with
the consolidated financial statements and the notes thereto included in the
Company's latest annual report on Form 10-K.

The condensed consolidated financial statements, in the opinion of management,
include all adjustments necessary to present fairly the Company's financial
position and the results of operations. These results are not necessarily to be
considered indicative of the results for the entire year.


 NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS (Unaudited)

1.       Nature of Operations and Significant Accounting Policies
         American Science and Engineering, Inc., is engaged in the development
         and manufacture of sophisticated X-ray inspection systems for critical
         detection and security screening solutions for sale primarily to U.S.
         and foreign government agencies.

         The significant accounting policies followed by the Company and its
         subsidiary in preparing its consolidated financial statements are set
         forth in Note 1 to the consolidated financial statements included in
         Form 10-K for the year ended March 29, 1996. The Company has made no
         change in these policies during this quarter.


2.       Inventories
         Inventories consisted of:
<TABLE>
<CAPTION>
                                                      Sept. 27, 1996       Mar. 29, 1996
                                                      --------------       -------------
<S>                                                     <C>                  <C>       
         Raw materials and completed
            sub-assemblies                              $2,706,000           $3,014,000
         Work in process                                 1,357,000            1,300,000
                                                        ----------           ----------
         Total                                          $4,063,000           $4,314,000
                                                        ==========           ==========
</TABLE>
         
3.       Income per Common and Common Equivalent Share
         Income per common share for the six month period ended September 27,
         1996 was computed by dividing net income by the weighted average number
         of common stock and common stock equivalents outstanding during the
         year. If dilutive, stock options and stock warrants were considered in
         the computation of earnings per common and common equivalent shares.


                                       -6-
<PAGE>   7
4.       Income Taxes
         At March 29, 1996, the Company had approximately $8,989,000 of federal
         net operating loss carryforwards which can be used, subject to certain
         limitations, to offset future federal taxable income. The carryforwards
         expire beginning in the year 1998 through the year 2010. The Company
         also has unused investment tax and other credits of approximately
         $235,000 expiring from 1997 through 2001. The provision for income
         taxes in the accompanying statement of income is substantially a
         current provision and differs from the provision calculated by applying
         the statutory federal income tax rate of 34% to income before provision
         for income taxes due to the following:


<TABLE>
<CAPTION>
                                                             Six Months Ended
                                                               Sept. 27, 1996
                                                             ----------------
<S>                                                              <C>       
          Provision for income taxes at statutory rate           $  305,000
          Benefit from net operating loss carryforward             (305,000)
          Other tax liabilities                                      39,000
                                                                  ---------
                                                                 $   39,000
                                                                  =========
</TABLE>


                                       -7-
<PAGE>   8
                     AMERICAN SCIENCE AND ENGINEERING, INC.
           ITEM 2 - MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                       CONDITION AND RESULTS OF OPERATIONS


Overview
In the Second quarter of fiscal 1997, the Company produced its sixth consecutive
quarter of increasing profits, was awarded two significant contracts totaling
$6.2 million and enhanced its liquidity position through a significant outside
financing transaction which will be discussed further in this section. Net sales
and contract revenues were $6,685,000 during the quarter, approximately equal to
the first quarter of fiscal 1997 and a 72% increase from the comparable year ago
period. The company earned net profits of $451,000 in the current quarter
compared to net profits of $406,000 in the previous quarter and net profits of
$155,000 in the corresponding year ago period.

Results of Operations
Net sales and contract revenues in the second quarter increased by $2,803,000
(72%) in comparison to the corresponding period a year ago and decreased by
$14,000 (.2%) compared to the first quarter of fiscal year 1997. Compared to the
previous quarter, security systems and related field service revenues were down
by $128,000 (2%) and research and engineering revenues were higher by $114,000
(26%). The increase in research and engineering revenues was due to the receipt
and start of two new contracts to build a second mobile CargoSearch(TM) vehicle
inspection system with enhanced operating and detection capabilities for the
Department of Defense Advanced Research Projects Agency. These two contracts
combined are valued at $2.7 million.

In addition to the above mentioned new contract awards, several other positive
developments occurred during the quarter, including a $3.5 million contract
extension to supply and install X-ray inspection systems for a high profile U.S.
Government investigative agency and customer delivery and acceptance of the
Company's first PalletSearch(TM) system.

For the second quarter, costs of sales and contracts increased to $4,329,000
from $2,577,000 in the corresponding period a year ago due primarily to
increased sales volume of X-ray inspection systems and field services revenues
in the current period. Costs of sales and contracts represented 65% of revenues
versus 66% for the corresponding period last year and 69% for the first quarter
of fiscal year 1997. The costs of sales percentage of revenues in the current
quarter decreased over the previous quarter primarily due to a change in the
sales mix.

Selling, general and administrative expenses of $1,473,000 for the second
quarter were higher by 53% compared to the corresponding year-ago period and
higher by 5% compared to the first quarter of fiscal 1997. As a percent of
sales, selling, general and administrative expenses were 22% of revenues in the
current quarter compared to 25% of revenues for the corresponding year-ago
period and 21% for the first quarter of fiscal year 1997. This declining ratio
of SG&A expenses to sales in the second quarter of fiscal 1997 versus the
year-ago period is primarily the result of higher revenues. As compared to the
first quarter of fiscal 1997, the increasing ratio of SG&A expenses to sales in
the second quarter of fiscal 1997 is primarily the result of increased sales and
marketing expenses.

Company-funded research and development expenses of $350,000 for the second
quarter were higher by $222,000 (173%) compared to the year-ago quarter and
higher by $106,000 (43%) compared to the first quarter of fiscal year 1997. This
increase is an intentional result of the Company's commitment to research and
development.

                                       -8-
<PAGE>   9
The Company produced a net profit of $451,000 during the second quarter. This is
an improvement of $296,000 over net profit in the year-ago quarter and an
improvement of $45,000 over the net profit reported in the first quarter of
fiscal 1997. The improved profitability results primarily from reduced costs of
sales and contracts partially offset by higher selling, general and
administrative expenses and Company funded research and development.

Liquidity and Capital Resources
Net cash used by operating activities during the first six months of fiscal year
1997 was $979,000, compared to $1,152,000 net cash used during the corresponding
year-ago period. Cash and cash equivalents decreased by $1,133,000 to $2,244,000
as of September 27, 1996, compared to $3,377,000 on March 29, 1996. Working
capital increased by $1,015,000 (15%) since March 29, 1996, growing from
$6,810,000 to $7,825,000 at the end of the second quarter.

No external borrowings were outstanding at the end of either the current or
previous quarter. Management believes the Company has access to sufficient
capital resources to support operations over the next several quarters.

During the quarter a line of credit for $2.5 million was closed with a local
bank. This line of credit is secured by eligible accounts receivable. Also
during the quarter, an additional $1.5 million borrowing facility was closed to
finance certain short lead-time orders the Company received during the quarter.
These new financing agreements replace the previous line of credit financing
agreements in place at March 29, 1996 and reported in the Company's latest
annual report on Form 10-K.


                                       -9-
<PAGE>   10
                     AMERICAN SCIENCE AND ENGINEERING, INC.

Part II - Other Information

Item 4.   Submission of Matters to a Vote of Security Holders.

The Special Meeting in Lieu of Annual Meeting of the Company was held on
September 26, 1996. At the meeting, all six of management's nominees to the
Board of Directors (Herman Feshbach, Al Gladen, Hamilton W. Helmer, Donald S.
McCarren, William E. Odom and Ralph S. Sheridan) were elected to a one year
term.

The stockholders also approved an amendment to the Company's Articles of
Organization ("Articles") limiting the liability of directors to the extent
permitted by Massachusetts law by a vote of 4,002,882 in favor to 71,250 opposed
and an amendment increasing the Company's authorized common stock, $.66 2/3 par
value, from 8,000,000 to 20,000,000 shares by a vote of 3,613,389 in favor to
459,998 opposed. In each case there were 20,000 broker non-votes.

The stockholders rejected six anti-takeover related proposals. The measures and
the votes in favor and against as well as broker non-votes are set forth below:

     4.  Amend the Articles to classify the Board of Directors into three
         classes;

     5.  Amend the Articles to increase the number of authorized shares of the
         Company's no par preferred stock from 100,000 to 1,000,000 shares and
         to amend the terms of the preferred stock;

     6.  Amend the Articles to require the vote of 66 2/3% of each class of
         outstanding stock to approve certain matters;

     7.  Amend the Company's By-Laws to require 90 day notice of any proposal by
         a stockholder to nominate candidates for director at the Annual
         Meeting;

     8.  Amend the By-Laws to require that special meetings of the stockholders
         may only be called by the President, a majority of directors or by
         stockholders holdings at least 50% of the Company's voting stock;

     9.  Amend the Articles to add a "fair price" amendment to the Articles of
         Organization.

<TABLE>
<CAPTION>
     Proposal Number                Votes For                 Votes Against              Broker Non-Votes
     ---------------                ---------                 -------------              ----------------
              <S>                   <C>                          <C>                        <C>
              4                     2,109,211                      461,381                  1,517,234
              5                     1,656,814                      831,903                  1,552,573
              6                     1,598,842                      960,643                  1,516,134
              7                     1,762,516                      801,894                  1,516,134
              8                     1,520,891                    1,038,927                  1,516,134
              9                     1,837,346                      734,518                  1,516,134
</TABLE>


                                      -10-
<PAGE>   11
Item 6.       Exhibits and Reports on Form 8-K

              (a)   Exhibit Index
                    Exhibit                                      Page
                    -------                                      ----
                    (11)    Statement re:  Computation of          6
                            Income per Common
                            and Common Equivalent Share

              (b)   Reports on Form 8-K

                    No reports on Form 8-K were filed during the quarter.



SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this Report to be signed on its behalf by the
undersigned hereunto duly authorized.


                               AMERICAN SCIENCE AND ENGINEERING, INC.
                               (Registrant)



Date: 31 October 1996          /s/ Lee C. Steele
                               __________________________________________
                               Lee C. Steele
                               Vice President and Chief Financial Officer


                                      -11-