<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 30, 1997
                                               ------------------

                                       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)

                                 (978) 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

                                                            Outstanding at
     Class of Common Stock                                  Sept. 30, 1997
     ---------------------                                  --------------
       $.66 2/3 par value                                      4,699,105


                               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. 30,        Sept. 27,         Sept. 30,      Sept. 27,
                                                              1997              1996             1997          1996
                                                           ---------        ---------         ---------      ---------
<S>                                                        <C>              <C>               <C>            <C>

 NET SALES AND CONTRACT REVENUE                             $8,705            $6,685            $16,237        $13,384
                                                            ------            ------            -------        -------

 COSTS AND EXPENSES:
   Cost of sales and contracts                               5,184             4,329              9,966          8,937
   Selling, general and administrative expenses              1,963             1,543              3,633          2,992
   Research and development                                    881               350              1,345            594
                                                            ------            ------            -------        -------
   Total costs and expenses                                  8,028             6,222             14,944         12,523
                                                            ------            ------            -------        -------

OPERATING INCOME                                               677               463              1,293            861
                                                            ------            ------            -------        -------

OTHER INCOME (EXPENSE):
   Interest, net                                                43                24                 70             71
   Other, net                                                   (8)              (17)               (11)           (36)
                                                            ------            ------            -------        -------
   Total other income (expense)                                 35                 7                 59             35
                                                            ------            ------            -------        -------

INCOME BEFORE PROVISION
   FOR INCOME TAXES                                            712               470              1,352            896

PROVISION FOR INCOME TAXES                                      27                19                 57             39
                                                            ------            ------            -------        -------

NET INCOME                                                  $  685            $  451            $ 1,295        $   857
                                                            ======            ======            =======        =======

INCOME PER SHARE - PRIMARY/FULLY
DILUTED                                                     $  .14            $  .09            $   .27        $   .18
                                                            ======            ======            =======        =======

DIVIDENDS PAID PER SHARE                                      NONE              NONE               NONE           NONE

WEIGHTED AVERAGE SHARES                 - PRIMARY            4,868             4,869              4,839          4,791
                                                            ======            ======            =======        =======
                                        - FULLY
                                          DILUTED            4,953             4,891              4,881          4,801
                                                            ======            ======            =======        =======

</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. 30, 1997     Mar. 28, 1997
                                                             --------------     -------------
                                                              (Unaudited)
<S>                                                          <C>                <C>

ASSETS       CURRENT ASSETS:
             Cash and cash equivalents                           $ 4,346           $ 3,202
             Accounts receivable, net                              6,704             5,019
             Unbilled costs and fees, net                          1,919               981
             Inventories                                           4,878             4,736
             Prepaid expenses and other current assets               262               157
                                                                 -------           -------
             Total current assets                                 18,109            14,095
                                                                 -------           -------

             NONCURRENT ASSETS:
             Deposits                                                 10               115
             Property and equipment, net of
                accumulated depreciation of
                $9,158 at Sept. 30,1997 and
                $8,860 at March 28,1997                            1,663             1,304
                                                                 -------           -------

                                                                 $19,782           $15,514
                                                                 =======           =======
</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. 30, 1997     Mar. 28, 1997
                                                             --------------     -------------
                                                              (Unaudited)
<S>                                                          <C>                <C>

LIABILITIES &   CURRENT LIABILITIES:
STOCKHOLDERS'   Current maturities of obligations
INVESTMENT        under capital leases                           $    18           $    18
                Accounts payable                                   3,187             2,253
                Accrued salaries and benefits                        838               573
                Accrued commissions                                  389                82
                Accrued warranty costs                               530               292
                Deferred revenue                                   1,050               526
                Other current liabilities                            633               495
                                                                 -------           -------
                TOTAL CURRENT LIABILITIES                          6,645             4,239
                                                                 -------           -------

                NONCURRENT LIABILITIES:
                Obligations under capital leases, net
                  of current maturities                               32                42
                Deferred revenue                                     547               660
                Deferred compensation                                167               174
                Deferred rent                                        265               249
                                                                 -------           -------
                TOTAL NONCURRENT LIABILITIES                       1,011             1,125
                                                                 -------           -------

                STOCKHOLDERS' INVESTMENT:
                Preferred stock, no par value
                Authorized - 100,000 shares
                Issued - None
                Common stock, $.66-2/3 par value
                Authorized - 20,000,000 shares
                Issued 4,669,105 shares at Sept. 30, 1997
                and 4,585,209 shares at Mar. 28, 1997              3,119             3,058
                Capital in excess of par value                    15,912            15,273
                Accumulated deficit                               (6,070)           (7,365)
                                                                 -------           -------
                                                                  12,961            10,966
                Note receivable-Officer                             (640)             (640)
                Less: treasury stock -73,157 and
                  62,481 shares at Sept. 30, 1997
                  and Mar. 28, 1997, at cost, respectively          (195)             (176)
                                                                 -------           -------

                TOTAL STOCKHOLDERS' INVESTMENT                    12,126            10,150
                                                                 -------           -------
                                                                 $19,782           $15,514
                                                                 =======           =======
</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. 30, 1997    Sept. 27, 1996
                                                                       --------------    --------------
<S>                                                                    <C>               <C>

Net income                                                                 $ 1,295          $   857
Adjustments to reconcile net income to net cash provided by
(used for) operating activities:
   Depreciation and amortization                                               304              162
   Provisions for contract, inventory, accounts receivable and
   warranty reserves                                                           665              (56)
Changes in assets and liabilities:
   Accounts receivable                                                      (1,685)          (1,861)
   Unbilled costs and fees                                                    (988)             220
   Inventories                                                                (342)             301
   Prepaid expenses, other current assets, and deposits                         --              122
   Accounts payable                                                            934              828
   Customer deposits                                                            --           (2,191)
   Accrued expenses and other current liabilities                            1,161              636
   Noncurrent liabilities                                                     (104)               3
                                                                           -------          -------
   Total adjustments                                                           (55)          (1,836)
                                                                           -------          -------

Net cash provided by (used for) operating activities                         1,240             (979)
                                                                           -------          -------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Purchase of property and equipment                                         (663)            (420)
                                                                           -------          -------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Proceeds from exercise of stock options                                     577              274
   Principal payments of capital lease obligations                             (10)              (8)
                                                                           -------          -------
   Cash (used for) provided by financing activities                            567              266
                                                                           -------          -------

NET INCREASE (DECREASE) IN CASH AND CASH
EQUIVALENTS                                                                  1,144           (1,133)
CASH AND CASH EQUIVALENTS AT BEGINNING OF PERIOD                             3,202            3,377
                                                                           -------          -------
CASH AND CASH EQUIVALENTS AT END OF PERIOD                                 $ 4,346          $ 2,244
                                                                           =======          =======

SUPPLEMENTAL DISCLOSURES OF CASH FLOW
INFORMATION:
   Interest paid                                                           $     3          $     3
   Income taxes paid                                                       $    --          $    30

NON-CASH TRANSACTIONS
   Issuance of stock in lieu of fees                                       $   104          $    --

</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 28, 1997.

       Effective quarter ended September 30, 1997, the Company has elected to
       change financial reporting from a fiscal month end to a calender month
       end. In addition, the year end reporting period will end on March 31,
       1998. This change in month end has no material effect on the results of
       operations for the quarter ended September 30, 1997.


2.     INVENTORIES
       Inventories consisted of:

<TABLE>
<CAPTION>
                                      Sept. 30, 1997       Mar. 28, 1997
                                      --------------       -------------
    <S>                               <C>                 <C>

    Raw materials and completed
       sub-assemblies                    2,733,000           3,106,000
    Work in process - CRAD               2,045,000           1,334,000
    Finished goods                         100,000             296,000
                                         ---------           ---------
    Total                                4,878,000           4,736,000
                                         =========           =========

</TABLE>



                                       -6-

<PAGE>   7




3.     INCOME PER COMMON AND COMMON EQUIVALENT SHARE

       Income per common share for the six month period ended September 30, 1997
       was computed by dividing net income by the weighted average number of
       common stock and common stock equivalents outstanding during the year.
       Stock options and stock warrants were considered in the computation of
       earnings per common and common equivalent shares.


4.     INCOME TAXES

       At March 28, 1997, the Company had approximately $6,986,000 of federal
       net operating loss carryforwards which can be used, subject to certain
       limitations, to offset future federal taxable income. The carryforwards
       expire through the year 2010. The Company also has unused investment tax
       and other credits of approximately $235,000 expiring 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. 30, 1997
                                                         ----------------
    <S>                                                  <C>

    Provision for income taxes at statutory rate             $ 460,000
    Benefit from net operating loss carryforward              (460,000)
    Other tax liabilities                                       57,000
                                                             ---------
                                                             $  57,000
                                                             =========

</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 1998, the Company produced its tenth consecutive
quarter of increasing profits. Net sales and contract revenues were $8,705,000
during the quarter, a 16% increase from the first quarter of fiscal year 1998
and a 30% increase from the comparable year ago period. The Company earned net
profits of $685,000 in the current quarter, a 12% increase from the previous
quarter net profits of $610,000 and a 52% increase from the comparable year ago
period net profits of $451,000.


RESULTS OF OPERATIONS
Net sales and contract revenues in the second quarter increased by $2,020,000
(30%) in comparison to the corresponding period a year ago and increased by
$1,173,000 (16%) compared to the first quarter of fiscal year 1998. Compared to
the previous quarter, security systems and related field service revenues
increased by $1,246,000 (19%) and research and engineering revenues were lower
by $73,000 (8%). The increase in security equipment and field service revenues
is primarily due to increased sales of x-ray equipment.

For the second quarter, costs of sales and contracts increased to $5,184,000
from $4,329,000 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 60% of revenues
versus 65% for the corresponding period last year and 63% for the first quarter
of fiscal year 1998. The costs of sales percentage of revenues in the current
quarter decreased over the previous quarter primarily due to increased sales
volume and a change in the sales mix.

Selling, general and administrative expenses for the second quarter were
$1,963,000, up from $1,543,000 in the corresponding period a year ago. As a
percent of sales, selling, general and administrative expenses were 23% of
revenues in the current quarter, 23% of revenues for the corresponding year-ago
period and 22% for the first quarter of fiscal year 1998. The quarter to quarter
increase in selling general and administrative expenses reflects an increased
level of international sales and marketing activities.

Company-funded research and development expenses of $881,000 for the second
quarter were higher by $531,000 (152%) compared to the year-ago quarter and
higher by $417,000 (90%) compared to the first quarter of fiscal year 1998. This
increase is a result of the Company's commitment to increased research and
development activity as well as the timing of certain development program
expenditures.

The Company produced a net profit of $685,000 during the second quarter. This is
an improvement of $234,000 (52%) over net profit in the year-ago quarter, and an
improvement of $75,000 (12%) over the net profit reported in the first quarter
of fiscal 1998. The improved profitability results primarily from reduced costs
of sales and contracts as a percentage of revenue, partially offset by higher
selling, general and administrative expenses and Company funded research and
development.


LIQUIDITY AND CAPITAL RESOURCES
Net cash provided by operating activities during the first six months of fiscal
year 1998 was $1,240,000, compared to $979,000 net cash used during the
corresponding year-ago period, primarily due to an improvement in net income,
higher non-cash adjustments to net income, and reduced customer deposits. Cash
and cash equivalents increased by $1,144,000 to $4,346,000 as of September 30,
1997, compared to $3,202,000 on March 28, 1997. Working capital increased by
$1,608,000 (16%) since March 28, 1997,

                                       -8-

<PAGE>   9



growing from $9,856,000 to $11,464,000 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 the Company negotiated an expanded credit facility agreement
with a local bank. The new facility runs through August 1998 and has two
components. The first component is a line of credit up to $4 million of base
borrowing capacity for either short-term working capital borrowing or issuance
of standby letters-of-credit. The second component is an additional $4 million
in excess standby letter-of-credit capacity to support foreign equipment sales.
This credit facility is secured by eligible accounts receivable and inventory.





                                       -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 30, 1997. At the meeting, all seven of management's nominees to the
Board of Directors were elected to a one year term according to the following
votes:


<TABLE>
<CAPTION>


                                                                 Votes
           Nominee                         Votes For           Withheld
           -------                         ---------           --------
           <S>                             <C>                 <C>

           Herman Feshbach                 3,998,380             44,321
           Al Gladen                       3,999,140             43,561
           Hamilton W. Helmer              3,999,235             43,466
           Donald S. McCarren              3,999,235             43,466
           William E. Odom                 3,999,235             43,466
           Ralph S. Sheridan               3,999,139             43,562
           Carl W. Vogt                    3,999,181             43,520

</TABLE>

                                      -10-

<PAGE>   11


Item 6.  EXHIBITS AND REPORTS ON FORM 8-K

         (a)   No exhibits are included.

         (b)   REPORTS ON FORM 8-K

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

               The information required by Exhibit Item 11 (Statement re:
               Computation of Income per Common and Common Equivalent Share) may
               be found in Footnote No. 4 on Page 7.


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: 30 October 1997                 /s/ Lee C. Steele
                                      ------------------------------------------
                                      Lee C. Steele
                                      Vice President and Chief Financial Officer



SAFE HARBOR STATEMENT
The foregoing 10-Q contains statements concerning the Company's financial
performance and business operations which may be considered "forward-looking"
under applicable securities laws.

The Company wishes to caution readers of this Form 10-Q that actual results
might differ materially from those projected in any forward-looking statements.

Factors which might cause actual results to differ materially from those
projected in the forward-looking statements contained herein include the
following: Significant reductions or delays in procurements of the Company's
systems by the United States Government; disruption in the supply of any
sole-source component incorporated into the Company's products (of which there
are several); litigation seeking to restrict the use of intellectual property
used by the Company; potential product liability claims against the Company;
global political trends and events which affect public perception of the threat
presented by drugs, explosives and other contraband; the ability of governments
and private organizations to fund purchases of the Company's products to address
such threats; and the potential insufficiency of Company resources, including
human resources, capital, plant and equipment and management systems, to
accommodate any future growth. These and certain other factors which might cause
actual results to differ materially from those projected are more fully set
forth under the caption "Risk Factors" in the Company's Registration Statement
on Form S-3 (SEC File No. 333-9151).

                                      -11-