<PAGE>
                                  EXHIBIT 10.4
                          SECOND AMENDED AND RESTATED
                            DUPONT PHOTOMASKS, INC.
                            NON-EMPLOYEE DIRECTORS'
                               STOCK OPTION PLAN
 
I. PURPOSE.
 
    The Purpose of the DuPont Photomasks, Inc. Non-Employee Directors' Stock
Option Plan (the "Plan") is to secure for DuPont Photomasks, Inc. (the
"Company") and its shareholders the benefits of the incentive inherent in
increased ownership of common stock, par value $.01 per share (the "Common
Stock"), of the Company by the members of the Board of Directors (the "Board")
of the Company who are not employees of the Company or any of its subsidiaries
("Non-Employee Directors"). It is expected that the Plan will encourage
qualified persons to become directors of the Company and that ownership of
Company stock will provide such Non-Employee Directors with a more direct stake
in the future welfare of the Company and encourage them to remain directors of
the Company.
 
II. ADMINISTRATION.
 
    The Plan shall be administered by the Board. The Board shall have all the
powers vested in it by the terms of the Plan, such powers to include authority
(within the limitations described herein) to prescribe the form of the agreement
embodying awards of stock options made under the Plan (the "Options") and the
power to determine the restrictions, if any, on the ability of participants to
dispose of any stock issued in the Plan. The Board shall, subject to the
provisions of the Plan, have the power to construe the Plan, to determine all
questions arising thereunder and to adopt and amend such rules and regulations
for the administration of the Plan as it may deem desirable. Any decisions of
the Board in the administration of the Plan, as described herein, shall be final
and conclusive. The Board may authorize any one or more of their number or the
Secretary or any other officer of the Company to execute and deliver documents
on behalf of the Board. The Board hereby authorizes the Secretary to execute and
deliver all documents to be delivered by the Board pursuant to the Plan. No
member of the Board shall be liable for anything done or omitted to be done by
such member or by any other member of the Board in connection with the Plan,
except for such member's own willful misconduct or as expressly provided by
statute.
 
III. AMOUNT OF STOCK.
 
    The stock which may be issued and sold under the Plan will be the Common
Stock (par value $.01 per share) of the Company. The total amount of stock for
which Options may be granted under the Plan shall not exceed 250,000 Common
Stock shares, subject to adjustment as provided in Article VI below. The stock
to be issued may be either authorized and unissued shares or issued shares
acquired by the Company or its subsidiaries.
 
IV. ELIGIBILITY.
 
    Each member of the Board of the Company who is not an employee of the
Company or any of its subsidiaries (a "Non-Employee Director") shall be eligible
to receive an Option in accordance with Article V below (provided such
Non-Employee Director is not precluded by his or her employer from receiving an
option grant). The adoption of this Plan shall be not deemed to give any
director any right to be granted an Option, except to the extent and upon such
terms and conditions, in accordance with terms of the Plan, as may be determined
by the Board.
<PAGE>
V. TERMS AND CONDITIONS OF OPTIONS.
 
    Each Option granted under the Plan shall be evidenced by an agreement in
such form as the Board shall prescribe from time to time in accordance with the
Plan, and shall comply with the following terms and conditions:
 
         1. The Option exercise price shall be the fair market value of the
    Common Stock shares subject to such option on the date the Option is
    granted, as determined in accordance with Article V9.
 
         2. Each Non-Employee Director shall receive an Option for 12,000 shares
    of Common Stock the later of: (a) upon his or her first election of the
    Board, or (b) the initial public offering of the Company's stock.
 
         3. Except as provided below, each year, as of the first day of the
    month following the Annual Meeting of Stockholders of the Company, each
    Non-Employee Director who has been reelected as a member of the Board as of
    the adjournment of the Annual Meeting shall receive an Option for 5,000
    shares of Common Stock; provided, however, that a Non-Employee Director who
    has been first elected to the Board within the 60 day period immediately
    preceding the Annual Meeting and has therefore received an Option under
    Article V2, above, shall not receive an Option for an additional 5,000
    shares at such Annual Meeting.
 
         4. Except as set forth in Article VII, the Option shall not be
    transferable by the optionee otherwise than by will or the laws of descent
    and distribution, and shall be exercisable during the lifetime of the
    optionee only by the optionee.
 
         5. No Option or any part of an Option shall be exercisable:
 
           A. After the expiration of ten years from the date the Option was
       granted;
 
           B.  Unless written notice of the exercise is delivered to the Company
       specifying the number of shares to be purchased and payment in full is
       made for the shares of Common Stock being acquired. Payment shall be made
       in cash (U.S. Dollars); and
 
           C.  Unless the person exercising the Option has been, at all times
       during the period beginning with the date of grant of the Option and
       ending on the date of such exercise, a Director of the Company or his
       permitted transferees (pursuant to Article VII), except that if such
       person shall cease to be such a Director by reason of Retirement or death
       while holding an Option that has vested under the terms of Article V6
       hereof but not expired and has not been fully exercised, such person or
       his permitted transferees (pursuant to Article VII), or in the case of
       death, the executors, administrators, legatees, or distributees, as the
       case may be, may at any time for a period of six months after the date
       such person ceased to be such a director (but in no event after the
       Option has expired under the provisions of Article V5A above), exercise
       the Option with respect to any shares of Common Stock as to which such
       person has not exercised the Option on the date the person ceased to be
       such a Director. In the event any Option is exercised by the executors,
       administrators, legatees or distributees of the estate of a deceased
       optionee, the Company shall be under no obligation to issue stock
       thereunder unless and until the Company is satisfied that the person or
       persons exercising the Option are the duly appointment legal
       representatives of the deceased optionee's estate or the proper legatees
       or distributees thereof.
 
         6. One-quarter (25%) of the total number of shares of Common Stock
    covered by the Option shall become exercisable beginning with the first
    anniversary date of the grant of the Option; thereafter an additional
    one-quarter (25% ) of the total number of shares of Common Stock covered by
    the Option shall become exercisable on each subsequent anniversary date of
    the grant of the Option until on the fourth anniversary date of the grant of
    the option the total number of shares of Common Stock covered by the Option
    shall become exercisable. In the event the Non-Employee Director ceases to
    be a Director by reason of Retirement or death, the total number of shares
    of
 
                                       2
<PAGE>
    Common Stock covered by the Option shall thereupon become exercisable
    provided such Option shall have been granted at least 6 months prior to such
    Retirement or death.
 
         7. Options granted to a person shall automatically be forfeited by such
    person if such person shall cease to be a Director for reasons other than
    Retirement or death.
 
         8. As used in this Article V, the term "Retirement" means the
    termination of a Director's service on the Board, including resignation from
    the Board upon reaching age 70 or otherwise resigning or not standing for
    reelection with the approval of the Board, but shall not include any
    termination of service resulting from an act of (I) fraud or intentional
    misrepresentation or (ii) embezzlement, misappropriation or conversion of
    assets or opportunities of the Company or any direct or indirect
    majority-owned subsidiary of the Company, by such Non-Employee Director. The
    determination of whether termination results from any such act shall be made
    by the Board, whose determination shall be conclusive.
 
         9. As used herein, fair market value shall be, at the time of the
    initial public offering of the stock, the initial offering price and
    thereafter shall be the average of the high and low prices of the Common
    Stock on the date of determination as reported on the NASDAQ Composite Index
    or if no sales of such stock were reported on the date of determination, the
    average of the high and low prices of such stock or the next preceding day
    on which sales were reported on such Index.
 
        10. Only non-qualified stock options may be granted under this plan.
 
VI. ADJUSTMENT IN THE EVENT OF CHANGE IN STOCK.
 
    1.  In the event of any stock dividend, split-up, reclassification or other
analogous change in capitalization, the Compensation Committee shall make such
adjustments, in the light of the change, as it deems to be equitable, both to
the optionees and to the Company, in
 
        A. The number of shares and prices per share applicable to outstanding
    stock options.
 
        B.  The aggregate limitation set forth in Article III with respect to
    the number of shares which may be made subject to options.
 
Furthermore, in the event of a distribution to common stockholders other than
interim or year-end dividends declared as such by the Board of Directors, the
Compensation Committee shall make such adjustments, in the light of the
distribution, as it deems to be equitable, both to the optionees and to the
Company, in respect of the items described in A above.
 
    2.  Any fractional shares resulting from adjustments made pursuant to this
Article shall be eliminated.
 
VII. MISCELLANEOUS PROVISIONS.
 
    1.  Except as expressly provided for in the Plan, no Non-Employee Director
or other person shall have any claim or right to be granted an Option under the
Plan. Neither the Plan nor any action taken hereunder shall be construed as
giving any Non-Employee Director any right to be retained in the service of the
Company.
 
    2.  All or a portion of the Option granted to a Non-Employee Director may be
on terms that permit transfer without consideration by such Non-Employee
Director to:
 
        (i) the spouse, children or grandchildren of the Non-Employee Director
    ("Immediate Family Members"),
 
        (ii) a trust or trusts for the exclusive benefit of such Immediate
    Family Members (including a custodian under a Uniform Gifts to Minors Act
    for the benefit of a child or grandchild), or
 
                                       3
<PAGE>
       (iii) a partnership or other entity in which such Immediate Family
    Members are the only partners, PROVIDED that (A) the stock option agreement
    pursuant to which such Options are granted must expressly provide for
    transferability in a manner consistent with this Section, and (B) subsequent
    transfers of transferred Options shall be prohibited except by will or the
    laws of descent and distribution. Following transfer, any such Options shall
    continue to be subject to the same terms and conditions as were applicable
    immediately prior to transfer, provided that for purposes of each agreement,
    the term "Non-Employee Director" shall be deemed to refer to the transferee
    (however, the events of termination of service as a director of Section V
    hereof shall continue to be applied with respect to the Non-Employee
    Director). Except as set forth above, an optionee's rights and interest
    under the Plan may not be assigned or transferred in whole or in part either
    directly or by operation of law or otherwise (except in the event of an
    optionee's death, by will or by laws of descent and distribution),
    including, but not by way of limitation, execution, levy, garnishment,
    attachment, pledge, bankruptcy, or in any other manner, and no such right or
    interest of any participant in the Plan shall be subject to any obligation
    or liability of such participant.
 
    3.  No Common Stock shares shall be issued hereunder unless counsel for the
Company shall be satisfied that such issuance will be in compliance with
applicable Federal, state and other securities laws and regulations.
 
    4.  It shall be a condition to the obligation of the Company to issue Common
Stock shares upon exercise of an Option, that the optionee (or any beneficiary
or person entitled to act under Article V5C above) pay to the Company, upon its
demand, such amount as may be requested by the Company for the purpose of
satisfying any liability to withhold Federal, state, local, or foreign income or
other taxes. If the amount requested is not paid (which payment may be made in
any manner prescribed in Article V5B), the Company may refuse to issue Common
Stock shares.
 
    5.  The expenses of the Plan shall be borne by the Company.
 
    6.  The Plan shall be unfunded. The Company shall not be required to
establish any special or separate fund or to make any other segregation of
assets to assure the issuance of shares upon exercise of any Option under the
Plan, and the issuance of shares upon exercise of Options shall be subordinate
to the claims of the Company's general creditors.
 
    7.  By accepting any Option or other benefit under the Plan, each optionee
and each person claiming under or through such person shall be conclusively
deemed to have indicated his or her acceptance and ratification of, and consent
to, any action taken under the Plan by the Company or the Board.
 
VIII. AMENDMENT OR DISCLOSURE.
 
    The Plan may be amended at any time and from time to time by the Board as
the Board shall deem advisable; provided, however, that no amendment shall
become effective without stockholder approval if such stockholder approval is
required by law, rule or regulation, and provided further, to the extent
required by Rule 16b-3 under Section 16 of the Securities Exchange Act of 1934,
as amended (the "Exchange Act"), in effect from time to time, Plan provisions
relating to the amount, price, and timing of Options shall not be amended more
than once every six months, except that the foregoing shall not preclude any
amendment to comport with changes in the Internal Revenue Code of 1986, the
Employee Retirement Income Security Act of 1974, or the rules thereunder in
effect from time to time. No amendment of the Plan shall materially and
adversely affect any right of any participant with respect to any Option
theretofore granted without such participant's written consent.
 
IX. EFFECTIVE DATE OF PLAN.
 
    The Plan shall become effective when the Plan is approved and adopted by the
Company's stockholders.
 
                                       4
<PAGE>
X. TERM.
 
    The Plan shall continue in effect without limit unless and until the Board
otherwise determines.
 
XI. COMPLIANCE WITH SEC REGULATIONS.
 
    It is the Company's intent that the Plan comply in all respects with Rule
16b-3 under the Exchange Act, and any related regulations. If any provision of
this Plan is later found not to be in compliance with such Rule and regulations,
the provision shall be deemed null and void. All grants and exercises of options
under this Plan shall be executed in accordance with the requirements of Section
16 of the Exchange Act and regulations promulgated thereunder.
 
XII. GOVERNING LAW.
 
    The validity and construction of the Plan and any agreements entered into
thereunder shall be governed by the laws of the State of Delaware.
 
                                       5